No evolutionary signature has been found in the complete proteomes of eukaryotes by now, although amino acid composition signature of the complete proteomes was discovered as molecular signature of the adaptation for thermophiles and halophiles. Arginine and lysine respectively have the guanidinium group and the ε-amino group as the ionizable side chain groups with different pKa values of about 12.5 and 10.5. The trends of their distribution seem similar in the range of about pIs﹤10.0 and diverge in the range of about pIs≥10.0 in most complete proteomes of 387 species from the three domains of life. The complete proteome of Reticulomyxa filose is the one of only in 287 eukaryotic complete proteomes that has a predominance of the trend of lysine over that of arginine in high pI proteins. The unbalanced distribution of the amino aicds(Arg, Lys) in high pI proteins of complete proteomes may originally come from different pKa values of arginine and lysine and be developed by the influences of an average lysine level of a proteome and evolution. Because of this unbalanced distribution, the pattern of arginine and lysine distribution in high pI proteins of some complete proteomes can form a particular proteomic structure as evolutionary signature that may be shaped by massive natural selection in molecular level from hundreds to ten thousands of proteins in the complete proteomes of many animals and green plants.