We investigate the ground-state energy of a two-dimensional Heisenberg antiferromagnet with competing nearest-and next-nearest-neighbor exchange interactions J 1 and J 2 . On the basis of a recently introduced cumulant technique we describe the transition from the usual antiferromagnetic phase to a so-called layered antiferromagnetic phase as a function of the ratio J 2 /J 1 . Whereas in the former phase the spins are approximately aligned antiparallel along the up and down sublattice, in the layered phase each of the two sublattices forms an antiferromagnetic lattice by itself. The result for the ground-state energy and for respective order parameters agree well with findings obtained from numerical methods. ͓S0163-1829͑97͒00937-5͔FIG. 1. Néel state for J 1 ӷJ 2 ͑left͒ and layered Néel state for J 2 ӷJ 1 ͑right͒.