Abstract A convergence analysis of a modified version of the least-squares recursive identification algorithm with forgetting factor is given. It is shown that the parametric distance converges to a zero mean random variable. It is also shown that, under persistent excitation condition on both system input and output, the condition number of the adaptation gain matrix is bounded. The variance of the parametric distance is bounded by the product of the noise variance times the upper bound of the condition number of the gain matrix. This is done by normalizing the measurement vector entering in the identification algorithm and by using a forgetting factor verifying λ t ⩽ 1 − ε; ε >0.