This letter presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper 1 for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval \p/fi2, Pl^i], with fii, ¡12 > 1, is proved to exceed its asymptotic value for a broader range of intervals than that given in the referred paper, and for any value of p. This extends the applicability of the estimator, relaxing the conditions that guarantee a given confidence level.