In this article, we discuss the normal complement problem for metacyclic groups in modular group algebras. If F is the field with p elements and G is a finite split metacyclic p-group of nilpotency class 2, then we prove that G has a normal complement in U(FG) For a finite field F of characteristic p, where p is an odd prime, we prove that D2pm has a normal complement in U(FD2pm) if and only if p = 3 and |F|=3.