In this paper, we address a problem of finding the optimum inner and outer code rates for a concatenated code in Gaussian binary symmetric channels. Clearly, as the inner code rate decreases, the error detection capability of the inner code increases. However, decreasing the inner code rate implies a decrease in error-correction capability of the outer code when overall code rate is fixed. With this notion in mind, we examine the optimum distribution of redundancy on the outer and inner codes to achieve a maximum performance gain in the concatenated coding scheme. Our analysis shows that the maximum coding gain can be obtained when the inner code rate is maximized and the outer code rate is minimized under the constraint of total code rate is fixed.