This paper presents a statistical sampling approach based on the multinomial distribution for obtaining a bound for either total population understatement or overstatement errors or both. The approach is nonparametric in nature and, unlike most currently used techniques, it has known characteristics so that the auditor is assured of the specified confidence level regardless of the nature of the population and the nature of the error pattern. Results are presented which show the multinomial bound to give tighter bounds than the Stringer bound in all instances stud]ed. The behavior of the multinomial bound is stud[ed with respect to the effects of sample size and error patterns.