Adaptive beamforming algorithms are often designed under the assumption that the sources illuminating the array are mutually uncorrelated. When the assumption is not valid, the performance of the adaptive beamforming algorithm in certain applications is severly limited. A simple example is included which illustrates how suppression of a look direction signal occurs when a power minimizing adaptive algorithm is used in the presence of correlated sources. This paper establishes certain properties of the eigenvectors of the correlation matrix of an array illuminated by a field of correlated discrete sources. On the basis of these properties an adaptive algorithm is proposed for resolving the direction of all discrete sources, even if they are mutually correlated. Simulation results are presented showing the performance of the algorithm proposed in this paper.