This paper proposes an efficient algorithm for the periodic discrete-time Riccati equation arising from a linear periodic time-varying system (A(k), B-k). Although the algorithm can be used for general problem, it is particularly efficient when A(k) is time-invariant and B-k is periodic, a special property associated with the problem of spacecraft attitude control using magnetic torques. We will compare the proposed algorithm, by using analysis and simulation, to some well-established algorithm to confirm our claim. Published by Elsevier Ltd.