Under sequential screening, a production lot is inspected item by item, and the decision is made after inspecting each item whether to inspect another item or to reject the remainder of the lot. Thus, uninspected items are never accepted. This screening process is a special case of the sequential sampling considered in Wortham and Wilson (1971). The process is formulated as an optimal stopping problem using a Bayesian approach. Based on an analysis of the structural properties of the optimal policy, a backward-recursive optimal algorithm that is more efficient than the existing algorithm for optimal sequential sampling is developed. The optimal policy will call for an early termination of the screening process on a lot with a high defective rate.