In the paper we present the results which enable to calculate the nonlinearity of round functions with quite large dimensions e.g. 32x32 bits, which are used in some block ciphers. This can be applied to improve the resistance of these ciphers against linear cryptanalysis. The involved method of calculating the nonlinearity is rested on the notion of multi-dimensional Walsh transform. At the end we give the application to linear cryptanalysis of the TGR block cipher.