In this paper, we revisit the problem of identifying multi-input/multi-output linear-time-invariant discrete-time systems from measured power spectrum data on uniform grids of frequencies studied by Van Overschee, De Moor, Dehandschutter, and Swevers (1997). We show that the algorithm proposed by these authors is not consistent. Then, we propose an interpolatory identification algorithm which is strongly consistent when the corruptions in the spectrum measurements have a bounded covariance function. The performance of the proposed algorithm is demonstrated in a simulation example. (C) 2010 Elsevier Ltd. All rights reserved.