This note considers the problem of identifying linear systems, where the input is observed in white noise but the output is observed in colored noise which also includes process disturbances. An efficient method is developed in this note, which can perform unbiased parameter estimation without utilizing a prefilter. The developed method is characterized by attractive features: direct use of the observed data without prefiltering; no need to evaluate autocorrelation functions for the input noise; no need to identify a high-order augmented system; and provision of a direct unbiased estimate of the system parameters without parameter extraction. Computer simulations are presented to illustrate its superior performance, including its significantly reduced computational complexity.