In the view point of practical engineering the identification problem may be considered as a problem to determine the optimal model in the sense of minimizing a given criterion function using the input-output records of the plant. In the system identification the statistical approach has been known to be very effective when the topological structure of the system and the statistical characteristics of the observation noises are known a priori. But in the practical situation there are many cases when the inforhation about the observation noises or the system noises are not available a priori. Here, the authors propose a new identification method which can be used effectively even in the cases when the variances of observation noises are unknown a priori. In the method, the identification of unknown parameters of a linear diserete system is achieved by minimizing the improved quadratic criterion function which is composed of the term of square equation errors and the term to eliminate the affection of observation noises. The method also gives the estimate of noise variance. Numerical computations for several examples show that the proposed procedure gives satisfactory results even when the short time observation data are provided.