Non-homologous isofunctional enzymes

Non-homologous isofunctional enzymes (NISE) are two evolutionarily unrelated enzymes that catalyzes the same chemical reaction. As the Enzyme Commission number (EC) is based on the reaction catalyzed by the enzyme, NISEs that catalyzed the same reaction would be assigned the same EC number, even though there may be no similarity in their protein sequences.

An example is of the enzyme urate hydroxylase (EC 1.14.13.113) which catalyzes the decomposition of urate, an important constituent of nitrogen cycling. The newly discovered HpyO gene was non-homologous in sequence to the original gene HpxO but yet shared certain characteristics enabling it to perform a similar reaction.

...
Wikipedia