This paper is concerned with the problem of optimal transmission of multi-dimensional Gaussian signals through a set of parallel channels with feedback. We especially consider the case where the feedback is corrupted by additive Gaussian noise. Under the constraint on the total power of the signals, we consider the problem of finding the optimal gain matrix, i.e., a set of optimal gains for the channels which maximizes, at each time, the decrease-rate of the estimation errors of the signals. The solution is given by computing the hypothetical optimal gain matrices for the two cases: we use the feedback; and we do not. The optimal gain matrix is determined by the fact which of the two hypothetical gain matrices gives the larger decrease-rate of the estimation errors.