Jean Harris, the Madeira School headmistress who last year was sentenced to 15 years to life in the shooting death of her lover, Dr. Herman Tarnower, lost another court battle today.

A five-judge panel of the Appellate Division of State Supreme Court in Brooklyn unanimously upheld Harris' conviction, ruling that her constitutional rights had not been violated at her sensational 14-week murder trial.

"We are convinced that although Jean Harris did not receive a perfect trial, she received an eminently fair one," presiding judge Milton Mollen wrote. "Nothing more is required."

There was no statement from Harris or from her defense attorney, Joel Aurnou. Aurnou, rushing from court to the Bedford Hills Correctional Facility where Harris reportedly has become a model prisoner, looked glum and had no comment for the press.

But attorney Harold Price Fahringer, who handled the appeal with Aurnou, said he was "deeply shocked" by the decision and said that both the attorney and Harris "expected we would win." Author Shana Alexander, who is writing a book on Harris and has been the only member of the press to visit her regularly, said she was personally "devastated" and Harris "surely must be."

"I visited her before Christmas and she said to me she was trying very hard not to hope," said Alexander. "I hope she tried hard enough."

Harris, the former head of the Madeira School for Girls in McLean, Va., was convicted last February of second-degree murder in the March 10, 1980, shooting of Tarnower, noted cardiologist and coauthor of "The Scarsdale Diet." The defense had argued that the shooting was a suicide attempt gone awry. Under her sentence, Harris, now 58, could not be paroled for 15 years.

In the appeal, which had gone on some six months, Harris' lawyers had argued that her rights had been violated when a police officer testified on a conversation he overheard between Harris and her lawyer after the shooting. The officer quoted her as saying "I think I've killed Hy Tarnower ."

They also argued that one of the jurors had a favorable and prejudicial link to the prosecution and that a surprise prosecution witness had been wrongly allowed to testify without the prior knowledge of Harris' attorney.

"Our strongest point was the conversation the police officer overheard," said Fahringer. "When a person goes to call their lawyer that is ordinarily a privileged conversation. This was one of the most blatant breaches I've ever seen."

The judges, however, disagreed, saying that the statement "neither indicates nor suggests an intent to kill on the part of Mrs. Harris. Indeed, it suggests the contrary since it reflects her surprise at Tarnower's condition."

Speaking on behalf of Harris, Fahringer said he planned "to exhaust appellate remedies" and insisted that he and his team believe "ultimately we'll prevail." He also said that in his visits with Harris she had "repeatedly expressed to me her outrage of the unfairness of the trial--that it was unfair from the very beginning with the terrible publicity that drenched the community with rumor and scandal."

Alexander echoed those views. The trial, she said, was "a monstrous injustice." She also spoke of Harris' adjustment to prison life, a life in which she serves as head of the Inmates Grievance Committee and teaches other prisoners.

"I think she was adjusting well. She was working, she was writing letters . . . . She wrote me a Christmas letter, a funny letter--she's a brilliant writer--a wonderful account of Christmas in Bedford and the children who came to visit their mothers; she cries when she talks about it, but she can still write a charming letter about it," said Alexander.

"I suppose the adjustment was based on the hope which she was trying not to hope," she said.