A non-stochastic state-space identification algorithm for linear time-invariant systems is modified for use with periodic linear systems. Like its predecessor, the modified algorithm forms block Hanker matrices from input-output data and uses the singular value decomposition of these Hankel matrices to compute state vector sequences. The state vector sequences are then used to compute system matrices associated with the periodic linear system by solving an (overdetermined) linear system. The modifications to the original algorithm are as follows. First, the periodic system of period p is viewed as p separate time-invariant period-mapped systems. This technique allows the structure of a periodic Hankel matrix to be deduced, which in turn allows a state vector sub-sequence for the periodic system to be computed. When a complete state vector sequence is computed, it is used directly to construct the periodic state-space models. Second, similarities in the structure of each of the periodic Hankel matrices associated with the p time-invariant period-mapped systems is exploited in such a way that not only reduces the amount of computation necessary, but also improves the accuracy of the computation of the system matrices.