This technical note presents a unified framework for bias compensation principle (BCP)-based methods applied for identification of linear systems subject to correlated noise. By introducing a non-singular matrix and an auxiliary vector uncorrelated with the noise, the unified framework is established. Since there are rich possibilities of the choices of the introduced matrix and vector, the proposed unified framework is very flexible. It can be verified that the existing BCP-based methods are special cases of the achieved result. It also shows that the unified framework can be used for deriving new or simplified versions of the BCP type methods.