A kernel in support vector machines can be described as a similarity measure between data, and this measure is used to find an optimal hyperplane that classifies patterns. It is therefore important to effectively incorporate the characteristics of data into the similarity measure. To find an optimal similarity between amino acid sequences, we propose a real exponent exponential form of the two metrices, which are derived from the evolutionary relationships of amino acids and the hydrophobicity of amino acids. We prove that the proposed metric satisfies the conditions to be a metric, and we find a relation between the proposed metric and the metrics in the string kernels which are widely used for the processing of amino acid sequences and DNA sequences. In the prediction experiments on the cleavage site of the signal peptide, the optimal metric can be found in the proposed metrics.