It is demonstrated that the premisses of the Einstein–Podolsky–Rosen paper are inconsistent when applied to quantum systems consisting of at least three particles. The demonstration reveals that the EPR program contradicts quantum mechanics even for the cases of perfect correlations. By perfect correlations is meant arrangements by which the result of the measurement on one particle can be predicted with certainty given the outcomes of measurements on the other particles of the system. This incompatibility with quantum mechanics is stronger than the one previously revealed for two-particle systems by Bell’s inequality, where no contradiction arises at the level of perfect correlations. Both spin-correlation and multiparticle interferometry examples are given of suitable three- and four-particle arrangements, both at the gedanken and at the real experiment level.