The directors of a health insurer that is trying to remake itself have picked a new board chairman.

HealthMarkets Inc., North Richland Hills, Texas, says the new chairman will be Allen Wise, who also is chairman of Coventry Health Care Inc., Bethesda, Md., and a director at Magellan Health Services Inc., Avon, Conn.

In the past, Wise was Coventry’s president. He also has been an executive vice president at UnitedHealth Group Inc., Minnetonka, Minn.

William Gedwed, who has been HealthMarkets’ board chairman and president, is giving up the title of chairman but will continue to be the company’s president.

The founder of the company and previous chairman, Ronald Jensen, 74, died in an automobile crash in Irving, Texas, in September 2005.

HealthMarkets once was UICI, a company that sold student health insurance, health insurance programs for the self-employed and the Star HRG limited-benefit medical plans.

Gedwed and other managers of UICI recently used private equity financing to buy control of the company. The managers have renamed the company, acquired a major player in the personal health account plan market, and sold the limited-benefit health plan unit to a division of CIGNA Corp., Philadelphia.