THE NEW AMERICAN TRADITION of parent-assassination takes a monster step forward with this book. Here there is no equivocation, no apology: William Saroyan was a bum and his 38-year-old son, Aram, is not ashamed to document every drop of his revenge. But before you ascend to any convenient moral heights and dump on such a traitorous kid -- as sentimental admirers of our one and only Armenian Mark Twain are already doing -- let it be said that this is an honest, even softly-shaded book, which permits its contempt to sting all the more.

Why have the floodgates opened towards the famous of a dying generation? More particularly, why have the sons and daughters of some of our best-loved national icons begun to pour out their secrets of bitterness and betrayal? One clear reason is the schizoid split between what the public knows of its idols and what the family has to live with. Since Americans attribute every unreal virtue to shimmering public figures, the absence of these qualities is felt with desperate incredulousness by the children. If Aram Saroyan is a good indicator, the sense of betrayal is all the greater because the father's or mother's "name" has practically crushed their own personalities, and then to have it worshipped for phony qualities is almost too much to bear.

Aram tells the story of his relationship, or non-relationship, with his father in the form of a loose diary that begins on April 14, 1981, when he hears that William Saroyan is dying of cancer. They've been out of touch for four years. It concludes a month later when the great-spirited prose singer of the American Depression bites the dust at the age of 72. The diary form gives young Saroyan -- a legitimate New York School poet in his own right, with no help or encouragement from his parent -- a chance to backtrack in time in order to trace out all the scars that now burn prominently as the elder Saroyan approaches death day by day.

Here is the gist of what Aram tells us. Although William Saroyan had little use for his son, considering him a hippie and a druggie whose own children bear names like Cream and Strawberry, the main reason he carried out a "lifelong, psychological war" against Aram and Aram's younger sister, Lucy, was because he detested the woman who bore them. Her maiden name was Carol Marcus, now Mrs. Walter Matthau, and Saroyan's almost pathological hatred of her was apparently predicated on three unforgiving "deceptions": (1) she passed herself off as an heiress, which she wasn't; (2) she was Jewish, and claimed that she wasn't; and (3), she was illegitimate, and didn't tell him.

At the time that Carol Marcus painted these lies for Saroyan, she was an insecure East Side-debutante type who was all of 17. Saroyan was almost twice her age, famous, gallant, erratically in love with this ripe young thing -- so much so that he married and divorced her twice by the time Aram was eight years old. What an accelerated start in life for any boy, even excluding all other traumas! At any rate, during the intermittent times in adolescence that the son saw his father, the latter would obsessively rave and rant to the emotionally paralyzed boy about his ex-wife. Aram came away with the definite feeling that William Saroyan ''wanted me and Lucy and my mother to die." No if's or but's.

Even if an embittered son is loading the deck in his treatment of his father, and this reviewer thinks not, there is a feeling of genuine shock when we first discover what a narrow-minded, old-country provincial Saroyan carried around inside his persona of democracy and gusto for all. If all the strict letter-of-the-law moralism had come from someone like T.S. Eliot, we would know how to handle it (although every report of Eliot in daily life has him behaving like a pussycat to Jews, poor people, illegitimates, homosexuals, etc.). But having all this fanatical, Ayatollah Khomeini stuff coming from a man like Williams Saroyan --"the author of The Human Comedy and The Time of Your Life, the wonderful crazy Armenian poet, the lover of life" -- knocks us off our pins until we comprehend what a tribal primitive Saroyan was beneath his California suntan.

But back to Aram's bitter and piercing account as his father approaches the end. When sister Lucy tries to visit the dying man at one of his two Fresno, California, homes, he tells her, "You've come here to exploit my death." He later gets a sweet message through to his son: "Tell Aram if he comes here he'll kill me." By this time the fading Saroyan has been installed in the local veteran's hospital, surrounded by the protective Armenian family tree, and Aram feels he has to crash through and make contact no matter what. He will drive down from Bolinas, California, in the north.

With wife and children, even with fear and trembling, he sees his shrunken father for the first time since their long separation. He kisses him and the older Saroyan draws his son to him in a hug. "Thank you, Aram," he says -- "his voice deep with emotion, the long-withheld words suddenly real now on the air." Then, if we can trust Aram's memory, William Saroyan speaks pure William Saroyan to his son as he lies dying: "it's the most beautiful time of my life . . . and death."

"For me, too, Pop," Aram says -- "now literally crying."

This is the high point of a very sad story, recorded in the diary entry for May 1, 1981. From then on it is downhill all over again. Even though Saroyan was to linger for almost another three weeks, there was only one more visit by Aram, after which Saroyan made it plain through intermediaries that he didn't want any more. He withdrew his offer permitting Aram and his family the use of one of the two Fresno houses while they visited -- houses stacked from floor to ceiling with Saroyan memorabilia, all signed and dated as if awaiting immediate transfer by the immortality trucking service.

William Saroyan's will turned out much as Aram thought it would. A tiny amount was left for Lucy and Aram and his family, just enough to serve "as a serious legal obstacle to contesting the will successfully." All the rest of Saroyan's possessions, properties, copyrights and future royalties were left to the William Saroyan Foundation. "In effect," says Aram, "he left his estate to himself. He took it with him."

Two final thoughts. Aram Saroyan sometimes sounds just a little superior to both his father and the rest of us, although one can forgive it in a flash after reading this bleak chronicle and realizing that the son had practically to invent himself in the face of a lifetime of his father's sneering rejections. And, lastly, there is something haunting and unanswered in the few words William Saroyan said to his lawyer, who suggested at the beginning of the death-watch that Lucy and Aram be informed.

"Oh no -- they hate me," the old man had said.

You can see that this tangled tragedy had indeed more than one side to it. Aram Saroyan has bravely, brilliantly, bloodily, shown us his. "Grandpa Bill" must remain, for him, uncharacteristically silent.