In this paper a simple sequential test is suggested. Distribution of the sample size, its moment generating function, the power function of the test, and the ASN (average sample number) function are obtained. The determination of the set of relative optimum zones for making decisions is shown to be unique. The existence of a class of sets of absolute optimum zones is proved. The suggested test is shown to be consistent. Some possible applications are discussed and a few numerical efficiencies are calculated.