Similar to the chaos game representation (CGR) of DNA sequences proposed by Jeffrey (Nucleic Acid Res. 18 (1990) 2163), a new CGR of protein sequences based on the detailed HP model is proposed. Multifractal and correlation analyses of the measures based on the CGR of protein sequences from complete genomes are performed. The Dq spectra of all organisms studied are multifractal-like and sufficiently smooth for the Cq curves to be meaningful. The Cq curves of bacteria resemble a classical phase transition at a critical point. The correlation distance of the difference between the measure based on the CGR of protein sequences and its fractal background is also proposed to construct a more precise phylogenetic tree of bacteria.