This paper presents a new Fiedler vector model for categorising amino acids, which is based on the Miyazawa-Jernigan matrix. The model splits the amino acid residues into two hydrophobic groups (LFI) and (MVWCY) and two polar groups (HATGP) and (RQSNEDK). In so doing, it independently confirms the findings of Wang and Wang and Cieplak et al. and demonstrates the validity of using eigenvectors to partition amino acid groups.