Let \mbox{\boldmath$X$} and \mbox{\boldmath$Y$} be stationarily cross-correlated multivariate stationary sequences. Assume that all values of \mbox{\boldmath$Y$} and all but one values of \mbox{\boldmath$X$} are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].