Motivated by an application of vibration analysis to gearbox fault surveillance, a new demodulation approach for gearbox vibration signals has recently been developed. Within this approach, the demodulation problem yields the study of a rank factorization problem for centrohermitian matrices. In this paper, using the properties of centrohermitian matrices, we first show that the rank factorization problem for centrohermitian matrices can be transformed into a rank factorization problem for real matrices. Based on previous works, we then show how to parametrize a class of centrohermitian solutions of the rank factorization problem that is important in practice.