Convergence proofs for least squares identification of weakly stationary processes have been published by several researches. The best known is that of Mann and Wald (1943) where an independent and identically distributed (i.i.d.) input is considered, and wherep-lim convergence is proved. Other proofs (Saridis and Stein 1908 also assume i.i.d. driving noise, though mean squares convergence is proved. In this paper no i.i.d. assumption is made but the more general bounded fourth moment white driving noise cases are covered, and a very short convergence proof is outlined. Convergence is shown to be in probability (p-lim), though under certain constraints almost sure convergence is also proved.