The standard semiclassical calculation of transmission correlation functions for chaotic systems is severely influenced by unitarity problems. We show that unitarity alone imposes a set of relationships between cross section correlation functions which go beyond the diagonal approximation. When these relationships are properly used to supplement the semiclassical scheme we obtain transmission correlation functions in full agreement with the exact statistical theory and the experiment. Our approach also provides a novel prediction for the transmission correlations in the case where time-reversal symmetry is present.