This talk is concerned with accurate computation of a product of two matrices whose entries are represented by floating-point numbers as defined by IEEE 754. Recently, we developed an error-free transformation of matrix multiplication. This transforms the product of two matrices by using only floating-point arithmetic. It is very useful to obtain an accurate approximation of the matrix multiplication. Moreover, since level 3 fraction is very high, the method can achieve high performance with high parallelism. We succeeded to improve the error-free transformation and give a validation method with diagonal scaling. The details of the method and numerical results will be presented in the presentation.