Estimation of the linear discriminant functionLis considered in the case where there aren1andn2observations from the populations II1and II2andMunclassified observations. Estimates ofLusing alln1+n2+Mobservations are proposed and evaluated in terms of the expected error rate under the assumption thatMis small relative ton1andn2. By appropriately weighting the sample means of the unclassified observations, an estimate ofLis given which dominates the usual estimate based on just then1+n2classified observations.