It is shown that the RP-HRP (random phase and higher random phase) approximation may be derived by a variational method. The reason why the secular equation of the RP-HRP approximation is nonhermitian is then made clear and a procedure which can lead it to be hermitian is suggested. It is further pointed out that the variation principle may also serve as a method to determine the average occupation numbers nr=0|fr-1∑μξrμ+ξrμ|Ψ0>.