A multiple testing method for examining factorial invariance for latent constructs evaluated by multiple indicators in distinct populations is outlined. The procedure is based on the false discovery rate concept and multiple individual restriction tests and resolves general limitations of a popular factorial invariance testing approach. The discussed method controls the overall significance level and is associated with higher power than conventional multiple testing procedures. The procedure avoids the necessity to choose a reference variable in applications of latent variable modeling for testing factorial invariance. The outlined method permits location of factorial invariance violations, in addition to its examination for a given set of construct indicators, and is illustrated with a numerical example. (Contains 4 tables and 1 note.)