Place the fish flat on a cutting board. Scale the fish with the backside of the knife.
Start the cut behind the dorsal fin perpendicular to the length of the fish and behind the gills. Angle in behind the skull (to miss as little meat as possible). Stop when the knife hits the backbone (actually in the center of the fish).
Insert the knife point into the cut you have made, with the blade flat and parallel to the working surface. Cut along the backbone to the tail of the fish.
Peel up the now-free flap of flesh. Cut all the way through to the belly of the fish, taking care to stay on the same side of the bones as you started, and cut back to the tail. This should free the first fillet.
Repeat on the other side. Cut off the tail remnants.