The well-known necessary and sufficient condition to find a solution to the robust strictly positive real(SPR) problem, namely, that the phase difference of the polynomials involved must be less than pi, was found to be also necessary and sufficient in the strengthened robust SPR problem by Anderson and Landau in a recent work, only for the continuous-time case. In this brief communication, we derive a necessary condition in the discrete-time case, which cannot be formulated in phase terms, and which is more stringent than the condition of the robust SPR problem, thereby establishing a fundamental difference between both continuous-time and discrete-time domains.