In the paper, the author presents and analyzes an algorithm for finding x and lambda such that Ax lambda Bx, where A and B are n x n matrices. The algorithm does not require matrix inversion, and may be used when either or both matrices are singular. The method is a generalization of Rutishausers LR method for the standard eigenvalue problem Ax lambda x and closely resembles the QZ algorithm given by Moler and Steward for the generalized problem given above. Unlike the QZ algorithm, which uses orthogonal transformations, the method, the LZ algorithm, uses elementary transformations. When either A or B is complex, the method should be more efficient.