Abstract: In this paper the least squares identification (LSI) of unknown coefficient matrices in the multi-dimensional dynamic system with uncorrelated noise is considered. Various conditions guaranteeing strong consistency of the LSI are put into comparison and the conditions proposed here and weaker than the previous one's are verified to be sufficient for the consistency of the LSI for which the asymptotic behaviors are also shown in the present paper. The main result is proved for the discrete-time system and its continuous-time analogue is also demonstrated.