In this paper we consider the optimum quantization of un- correlated discrete stochastic signals characterized by it PDF (Probability Distribution Function). The quantizer is design to maximize the preservation of information from the original signal to the quantized signal. We present a simple characterization of the quantization intervals and the corresponding quantization values. It is shown that the optimum quantization characteris- tic is in general non-uniform and the optimum quantiza- tion intervals depend on the PDF of the stochastic to be quantized, with smaller quantization intervals (and, conse- quently, smaller quantization errors) in the regions where the PDF takes higher values (i.e., for the values that are more likely to occur. This contrasts with conventional non- uniform quantization characteristics where we have smaller quantization intervals for signals with smaller amplitude, regardless of its PDF.