The central question in the origin of life is to understand how structure can emerge from randomness. The Eigen theory of replication states, for sequences that are copied one base at a time, that the replication fidelity has to surpass an error threshold to avoid that replicated specific sequences become random because of the incorporated replication errors [M. Eigen, 58 (10), 465-523 (1971)]. Here, we showed that linking short oligomers from a random sequence pool in a templated ligation reaction reduced the sequence space of product strands. We started from 12-mer oligonucleotides with two bases in all possible combinations and triggered enzymatic ligation under temperature cycles. Surprisingly, we found the robust creation of long, highly structured sequences with low entropy. At the ligation site, complementary and alternating sequence patterns developed. However, between the ligation sites, we found either an A-rich or a T-rich sequence within a single oligonucleotide. Our modeling suggests that avoidance of hairpins was the likely cause for these two complementary sequence pools. What emerged was a network of complementary sequences that acted both as templates and substrates of the reaction. This self-selecting ligation reaction could be restarted by only a few majority sequences. The findings showed that replication by random templated ligation from a random sequence input will lead to a highly structured, long, and nonrandom sequence pool. This is a favorable starting point for a subsequent Darwinian evolution searching for higher catalytic functions in an RNA world scenario.