The original ergodic interference alignment scheme proposed by Nazer et al. requires symmetric channel phase distribution. In this paper, we investigate a new ergodic interference alignment scheme which can achieve one half interference-free degree of freedom (DoF) for arbitrary phase distribution. Even for symmetric phase distributions, the new scheme achieves a better high SNR offset than the original ergodic interference alignment scheme, and depending upon the magnitude distributions it is shown that the SNR offset improvement with the new scheme over the original scheme can be arbitrarily large. The SNR offset optimal ergodic alignment scheme is based on results in majorization theory.