All the Young Men(1960)

During the Korean War, the lieutenant in charge of a Marine rifle platoon is killed in battle. Before he dies, he places the platoon's sergeant, who's black, in charge. The sergeant figures on having trouble with two men in his platoon: a private who has much more combat experience than he does, and a racist Southerner who doesn't like blacks in the first place and has no intention of taking orders from one.