A bilinear multivariate errors-in-variables model is considered. It corresponds to an overdetermined set of linear equations AXB=C, A?Rm×n, B?Rp×q, in which the data A, B, C are perturbed by errors. The total least squares estimator is inconsistent in this case. An adjusted least squares estimator hat X is constructed, which converges to the true value X, as m -> infty, q -> infty. A small sample modification of the estimator is presented, which is more stable for small m and q and is asymptotically equivalent to the adjusted least squares estimator. The theoretical results are confirmed by a simulation study.