That fat people are jolly is almost certainly a myth, but a study published yesterday has found a strong association between higher body mass index, or B.M.I., and lower risk of suicide.

In a 16-year study that followed more than 45,000 male health professionals, researchers found a steady decrease in suicides as B.M.I. increased, even after controlling for variables including smoking, dietary factors, physical activity, marital status and alcohol use. There were 131 suicides during the time of the study.

Compared with those in the lowest 20 percent in B.M.I., men in the highest one-fifth were almost 60 percent less likely to kill themselves.

''It's a surprisingly strong relationship,'' said Kenneth J. Mukamal, the lead author and an associate professor of medicine at Harvard University. ''But even though we see that heavier men are less likely to commit suicide, there are plenty of other studies that link obesity to poor health. Gaining weight is not the best way to improve anyone's mental health. I hope these findings will provide insight into new strategies to prevent suicide.''

The authors, writing in The Archives of Internal Medicine, suggest that B.M.I. could be linked to suicide through circulating levels of insulin, which may have a role in determining mood.

The authors point out that depression and the medicines used to treat it may themselves lead to higher B.M.I., and that the relationship among depression, antidepressant medicine and the risk of suicide is complex. They also acknowledged that they did not have information on suicide attempts, and that the group they studied was not necessarily representative of the general population.