This note considers the bias-eliminating least squares (BELS) method for identifying the errors-in-variables systems with white input noise and colored output noise. A simplified form of the BELS algorithm is proposed that is proved to be equivalent to the existing one. Some expositions of this simplified BELS expression are also given. The new relation is a form of linear IV equations which will not only reduce the computational load but also simplify the analysis of the properties of the BELS estimates.