THERE MUST HAVE BEEN an easier way to fire Joe Califano.And, of course, there was - at any of the innumerable points along the way when Mr. Califano affronted his boss. The story is that some show was regarded as necessary to demonstrate to other willful and (a new concept for the Carter administration) disloyal Cabinet members that there were limits.But the shape-up-or-ship-out signal was at least partially muted by the news that Patricia Harris, secretary of HUD, has been selected to take Mr. Califano's job. Of all the many things people have said about Mrs. Harris during a full, rich and combatloaded career in public life, one has never been that she was reluctant to speak her mind or have her way; and in that place on the new evaluation form where the evaluator is meant to list weaknesses, you'd better believe "docility" is not going to appear on hers. Our guess is that Mrs. Harris is also not going to turn out to be all that different from Mr. Califano on substantive policy questions; they haven't been so far.

So what was the Califano firing about? What was the trouble? Personal reasons, most assuredly - a style and a temperament that gave particular offense to his White House patrons, a kind of pushy, abrasive, round-the-clock quality that never seemed content to let things be and that couldn't ever take "no" for an answer, striving ceaselessly and infuriatingly to get it pressured and bargained back to at least "Not now, perhaps, but soon" or "Maybe, just a little bit." Mr. Califano was and is also the complete Washington political man, attached to his telephone as to a life-support system, somehow mixing into everything. Washington politics, lately anathematized once again by the president, drips from Mr. Califano. This was not calculated to please the Carter White House either.

Two things need to be said about these chemical and metabolic attributes of Mr. Califano. One is that they are not necessarily very endearing. The other is that they have probably been the most useful thing about him at HEW. That has been a mess of a department and one charged with administering some of the biggest and certainly most politically tricky and divisive programs the mind of legislative man ever devised - and also some of the most important. Mr. Califano, as an advocate of social welfare measures and a proponent of Great Society values, has been too gung-ho for some tastes - including, from time to time, our own. That is what earned him much of the opprobrium in various sectors of the electorate that the president apparently told Mr. Califano made him an intolerable political liability, in addition to displeasing the Carter staff.

But that is also what accounted for Mr. Califano's most valuable public service: his energetic commitment to furthering the claims of health, education and welfare on the public purse and the public conscience. The constituents of HEW and the values it is meant to reflect both had an aggressive and powerful friend in the secretary. One of the reassuring aspects of this whole convulsive week is that Mrs. Harris, who will replace him, shares many of Mr. Califano's most annoying and useful faults.