The critical behavior of an m‐vector model with random impurities is investigated through the use of renormalization group techniques near four dimensions. For almost all values of m, this disordered model has two stable fixed points and a single nontrivialy unstable fixed point. The model exhibits sharp phase transitions with exponents which do not depend continuously on the concentration of impurities. The familiar m‐component fixed point, which is normally assumed to characterize the critical behavior of the pure m‐vector model, is unstable whenever m%4.