In Paturi, Pudlák, Saks, and Zane (Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science (FOCS1998), pp. 628–637, 1998) proposed a simple randomized algorithm for finding a satisfying assignment of a k-CNF formula. The main lemma of the paper is as follows: Given a satisfiable k-CNF formula that has a d-isolated satisfying assignment z, the randomized algorithm finds z with probability at least $2^{-(1-\mu_{k}/(k-1)+\epsilon_{k}(d))n}$ , where $\mu_{k}/(k-1)=\sum_{i=1}^{\infty}1/(i((k-1)i+1))$ , and ϵ k (d)=o d (1). They estimated the lower bound of the probability in an analytical way, and used some asymptotics. In this paper, we analyze the same randomized algorithm, and estimate the probability in a combinatorial way. The lower bound we obtain is a little simpler: $2^{-(1-\mu_{k}(d)/(k-1))n}$ , where $\mu_{k}(d)/(k-1)=\sum_{i=1}^{d}1/(i((k-1)i+1))$ . This value is a little bit larger (i.e., better) than that of Paturi et al. (Proceedings of the 39th Annual IEEE Symposium on Foundations of Computer Science (FOCS1998), pp. 628–637, 1998) although the two values are asymptotically equal when d=ω(1).