Disclosed is an isolated or purified peptide consisting of the amino acid sequence shown in SEQ ID NO: 3. Also disclosed is a composition comprising a peptide consisting of the amino acid sequence shown in SEQ ID NO: 3 and further comprising a peptide consisting of the amino acid sequence shown in SEQ ID NO: 1 and/or a peptide consisting of the amino acid sequence shown in SEQ ID NO: 2. Further disclosed is a method for preparing a peptide for improving brain function, comprising: hydrolysing milk casein with an enzymatic catalyst comprising an alkaline protease derived from Bacillus licheniformis, an alkaline protease derived from Aspergillus sp., or a neutral protease derived from Aspergillus melleus to produce a hydrolysate comprising: (i) a peptide consisting of the amino acid sequence shown in SEQ ID NO: 1, (ii) a peptide consisting of the amino acid sequence shown in SEQ ID NO: 2, or (iii)a mixture of the peptides of (i) and (ii), wherein the production yield of each of the peptides is 2% or more, or the total production yield of the mixture is 10% or more wherein the sequences are as defined in the specification.
