In this paper we present a modification of alternating least squares (ALS) for tensor canonical polyadic approximation that takes into account mutual coherence constraints. The proposed algorithm can be used to ensure well-posedness of the tensor approximation problem during ALS iterates and so is an alternative to existing approaches. We conduct tests with the proposed approach by using it as initialization of unconstrained alternating least squares in difficult cases, when the underlying tensor model factors have nearly collinear columns and the unconstrained approach is prone to a degenerate behavior, failing to converge or converging slowly to an acceptable solution. The results of the tested cases indicate that by using such an initialization the unconstrained approach seems to avoid such a behavior.