A Heisenberg ferromagnet is considered in which the eigenvalues of S^z and (S^z)² are 1, 0, - lambda and 1, 0, lambda ² where lambda is the asymmetry parameter lying between 0 and 1. It is shown that in this system a quadrupolar phase appears as an intermediate phase even when the ground state is ferromagnetic. The temperature T_q at which the transition from the ferromagnetic to the quadrupolar phase occurs is derived with a molecular-field approximation. Two limiting cases lambda to 0 and lambda to 1 are also examined.