A self-replicating RNA ligase ribozyme was converted to a cross-catalytic format whereby two ribozymes direct each other's synthesis from a total of four component substrates. Each ribozyme binds two RNA substrates and catalyzes their ligation to form the opposing ribozyme. The two ribozymes are not perfectly complementary, as is the case for replicating nucleic acid genomes in biology. Rather, the ribozymes contain both template elements, which are complementary, and catalytic elements, which are identical. The specificity of the template interactions allows the cross-catalytic pathway to dominate over all other reaction pathways. In the presence of $2{\mu}M$ each of the corresponding substrates, one ribozyme catalyzes the synthesis of the second ribozyme with an initial rate of $6.8{\times}10^{-3}\;min^{-1}$, while the second ribozyme catalyzes the synthesis of the first with an initial rate of $2.9{\times}10^{-3}min{-1}$. As the concentration of the two ribozymes increases, the rate of formation of additional ribozyme molecules increases, consistent with the overall autocatalytic behavior of the reaction system. Here, I present results that possibly demonstrate a clue for a self-replicating molecule by showing an RNA ligase ribozyme, which is reminiscent of 'Prebiotic Era'.