The μ-e symmetry is destroyed by the anomalous interaction. We discuss the influence of the anomalous interaction on the weak-processes, and analyse the relation between the renormalization of the weak-interaction constant and such properties of the anomalous interaction as the charge independence and the γ5-transformation. The re-normalized constants are shown to be GV=G,GA=εG,ε=1+δ. This result is used to solve the difficulty which occurs when one uses the universal V-A Fermi weak-interaction theory and the conserved vector current hypothesis to explain the lifetime of the muon. Comparing the thory with various experiments, we obtain δ = 0.04, which may be interpreted as the experimental limitation of the μ-e symmetry.