The singularity problem of the constant modulus algorithm (CMA) equalizer may be overcome by implementing the CMA equalizer as a two-stage equalizer, with the first stage being a modified version of a CMA equalizer and the second stage being a conventional CMA equalizer. The first stage may be made up of four sub-equalizers, of which only two of the sub-equalizers are independent, i.e., uncorrelated to each other. This first stage equalizer may compensate for PMD. The second stage equalizer is a conventional CMA equalizer made up of four sub-equalizers that are adjusted independently. This second stage equalizer may compensate for polarization-dependent loss (PDL) and any residual CD that is not fully compensated for by a CD compensator before the two-stage equalizer. Advantageously, as the determinant of the first stage never approaches zero, the singularity problem of a conventional CMA single-stage-only equalizer is avoided by the two-stage equalizer.