This paper describes a new structural reliability analysis iteration procedure based on the concept of most probable point locus (MPPL). Using a new quadratic search algorithm, the proposed procedure examines the global behavior of the limit-state function, g, along the MPPL in the standard normal space in search of the most probable point (MPP) on the g = o surface, and identifies unusual conditions such as multiple MPPs. During the iteration procedure, the generated information is updated after each sensitivity analysis. This action helps the analyst to minimize the number of computer runs and determine the next step. By adopting two efficient convergence criteria, the proposed procedure is demonstrated to be significantly more efficient than the commonly used reliability analysis procedures, and is suitable to be integrated with existing general-purpose finite element computer programs for nondeterministic structural analysis.