The Lanczos algorithm for nonsymmetric matrices is studied. It is shown how breakdown caused by a pair of corresponding basis vectors being orthogonal can be remedied by computing further vectors in the Krylov sequences. This corresponds to performing
pivots when factorizing the moment matrix, which may be indefinite for nonsymmetric eigenproblems. It is stated that when
pivots are insufficient to continue the process, all eigenvalues have converged. Results of a few numerical tests are reported.