Empty the black water tank with the bad valve while wearing rubber gloves. Follow the RV manufacturer's instructions for emptying and where to dispose of the waste.
Pour five or more gallons of water into the toilet of your RV, let it sit for several minutes and inspect both valves for leaking water to determine the faulty valve.
Drain the tanks again, unscrew the four screws attaching the leaky valve to the tank and the waste water line and remove the flanges, the valve and the rubber seals in the valve's gasket groove. Discard the old valve and gaskets.
Screw in the new valve with the new rubber seals. Check to ensure the correct placement of the gaskets in the new valve, or the new valve will also leak after being installed. Follow the instructions for installation that come with the valve.
Pour five gallons of water into the toilet, wait about 10 minutes, and check the new valve to make sure it's not leaking and is working properly.