This paper concerns with signal cancellation problem in a linearly constrained adaptive array processor in coherent environment. Alternate mainbeam nulling approach was proposed to prevent the signal cancellation phenomenon. The linearly constrained LMS algorithm with a unit gain constraint and that with a null constraint in the direction of the desired signal is alternately implemented to reduce the signal interaction between the desired signal and the interferences, which is the main cause of the signal cancellation. It is shown that the proposed method performs better than a conventional method.