A cooling system for a marine engine is provided with various cooling channels which allow the advantageous removal of heat at different rates from different portions of the engine. A split flow of water is conducted through the cylinder head, in opposite directions, to individually cool the exhaust port and intake ports at different rates. This increases the velocity of coolant flow in the downward direction through the cylinder head to avoid the accumulation of air bubbles and the formation of air pockets that could otherwise cause hot spots within the cylinder head. A parallel coolant path is provided so that a certain quantity of water can bypass the engine block and avoid overcooling the cylinder walls.