Harlem-born LeTang, the son of Caribbean-born parents Clarence and Marie LeTang, began dancing at age seven and opened his first New York City studio when he was 17. His earliest pupils included Broadway and film stars Betty Hutton and Clifton Webb. He went on to teach a wide range of entertainers, including Lena Horne, Milton Berle, Bette Midler, Sugar Ray Robinson and Billie Holiday, as well as the famed tap-dancing brothers Gregory and Maurice Hines.
Mr. LeTang would choreograph the tap steps executed by the Hines brothers in the hit 1979 revue Eubie!, which spotlighted the music of Eubie Blake. (Blake and LeTang had first worked together on the 1952 Broadway revue Shuffle Along.) He worked with Gregory Hines again in 1981 in another successful Broadway revue, Sophisticated Ladies, working in tandem with co-choreographer Michael Smuin.
He was nominated for Tony Awards for both shows. He won the honor for his last Broadway show, the 1989 revue Black and Blue. The cast included Savion Glover, the current standard-bearer in the tap world, and thus the long arm of Mr. LeTang's influence was extended another generation.
Mr. LeTang worked on a few earlier Broadway shows, including My Dear Public (1943), Dream With Music (1944), in which he worked alongside George Balanchine, and Shuffle Along (1952). He also choreographed the Tin Man's number "Slide Some Oil on Me" in The Wiz.
He moved in 1992 to Las Vegas, where his Cotton Club Revue ran in 1985 at the Aladdin and the Dunes. Film work included the movies "Tap" and "The Cotton Club," in which he appeared on screen. He was nominated for an Emmy for his choreography of the 2001 TV film "Bojangles."
During his long career, Henry LeTang met almost everyone in his field, including the legendary tapper Bill "Bojangles" Robinson, who was said to have observed of Mr. LeTang: "That young man's staging is really copasetic."