An L-methionine γ-lyase having modified function which is obtained by structurally stabilizing natural L-methionine γ-lyase by analyzing the structure of crystals thereof by using X-ray, estimating an amino acid sequence concerning its substrate specificity and varying amino acid residue thereof enzymes comprising a protein constituting the L-methionine γ-lyase having modified function or its multimer (preferably its tetramer) DNA sequences encoding these enzymes a process for producing these enzymes and medicinal preparations (preferably anticancer agent) containing these enzymes.