A signal space diversity (SSD) scheme is one of techniques to achieve diversity gain in fading channels. This method consists of two key operations: constellation rotation and component-wise interleaving. Because of these operations, the decision boundaries for the SSD are no longer perpendicular, and thus, different coordination approaches are required for the analysis of error rates compared to conventional rectangular coordinates. In this paper, we derive an exact expression of the symbol error rate for the SSD scheme in Rayleigh fading channels for 4QAM and 16QAM. By defining the ratio of the standard deviation of the inphase and quadrature components, we intruduce a new signal model for the SSD. Based on this signal model, we can compute the exact symbol error rate using polar coordinates. The computer simulation results confirm the accuracy of our analysis for Rayleigh fading channels.