In "Centrohermitian solutions of a factorization problem arising in vibration analysis. Part I: Lee's Transformation", we showed that the structure of centrohermitian matrices and Lee's transformation can be used to transform the search for centrohermitian solutions of a rank factorization problem -- at the core of a new demodulation approach arising in gearbox vibration analysis -- into the search for real solutions of a polynomial system. Hence, in "Centrohermitian solutions of a factorization problem arising in vibration analysis. Part I: Lee's Transformation", we parametrized a class of centrohermitian solutions of the rank factorization problem that is interesting in practice. Despite its effectiveness, Lee's transformation can be seen as a black box hiding information on the resolution of the rank factorization problem for centrohermitian solutions. To get more insight, in this paper, we develop an alternative approach to the centrohermitian rank factorization problem.