Transition probability matrices of amino acid substitution are calculated for hemoglobin, cytochrome c, fibrinopeptide, immunoglobulin and lysozyme, and for protein as a whole. When these matrices operate on the column vectors which represent the contemporary amino acid frequencies of the corresponding proteins, amino acid compositions change so as to increase their entropy. The entropy increase of amino acid sequences in proteins need not be interpreted as a random process. If we assume instead a selective process favoring randomness in protein, the biased nature of the genetic code can contribute to non-randomness in the DNA sequence. The entropy increase of protein as a whole is interpreted as a diversification of protein, and is reflected in DNA base sequence of higher organisms.