Multistable systems can exhibit stochastic resonance which is characterized by the amplification of small periodic signals by additive noise. Here we consider a nonmultistable linear system with a multiplicative noise forced by an external periodic signal. The noise is the sum of a colored noise of mean value zero and a noise with a definite sign. We show that the system exhibits stochastic resonance through the numerical study of an exact analytical expression for the mean value obtained by functional integral techniques. This is proof of the effect for a very general kind of noise which can even have a definite sign.