A component of the CLASSICAL COMPLEMENT PATHWAY. C2 is cleaved by activated COMPLEMENT C1S into COMPLEMENT C2B and COMPLEMENT C2A. C2a, the COOH-terminal fragment containing a SERINE PROTEASE, combines with COMPLEMENT C4B to form C4b2a (CLASSICAL PATHWAY C3 CONVERTASE) and subsequent C4b2a3b (CLASSICAL PATHWAY C5 CONVERTASE)