The convergence of the solution of the differential and difference periodic Riccati equation with non-negative initial condition is studied. In particular, with reference to the Riccati equation for optimal filtering, we consider detectable but not necessarily stabilizable systems and no restrictive assumption is imposed on the modulus of the unreachable characteristic multipliers. Then, a new condition for the convergence to the periodic strong solution is provided. As a corollary, it follows that, for any positive definite initial condition, the solution of the periodic Riccati equation converges to the periodic strong solution. The new condition encompasses as particular cases the convergence results already available in the literature.