We have previously postulated a novel hypothesis for the origin of life, assuming that life on the earth originated from "[GADV]-protein world", not from the "RNA world" (see Ikehara's review, 2002). The [GADV]-protein world is constituted from peptides and proteins with random sequences of four amino acids (glycine [G], alanine [A], aspartic acid [D] and valine [V]), which accumulated by pseudo-replication of the [GADV]-proteins. To obtain evidence for the hypothesis, we produced [GADV]-peptides by repeated heat-drying of the amino acids for 30 cycles ([GADV]-P(30)) and examined whether the peptides have some catalytic activities or not. From the results, it was found that the [GADV]-P(30) can hydrolyze several kinds of chemical bonds in molecules, such as umbelliferyl-beta-D-galactoside, glycine-p-nitroanilide and bovine serum albumin. This suggests that [GADV]-P(30) could play an important role in the accumulation of [GADV]-proteins through pseudo-replication, leading to the emergence of life. We further show that [GADV]-octapaptides with random sequences, but containing no cyclic compounds as diketepiperazines, have catalytic activity, hydrolyzing peptide bonds in a natural protein, bovine serum albumin. The catalytic activity of the octapeptides was much higher than the [GADV]-P(30) produced through repeated heat-drying treatments. These results also support the [GADV]-protein-world hypothesis of the origin of life (see Ikehara's review, 2002). Possible steps for the emergence of life on the primitive earth are presented.