Cooling fan does NOT stop

1986 Porche 944 with 106,000 miles. I recently had the battery replaced. Then the next time I went to drive it the battery was dead again. I was told the reason the battery died was not the alternator, but was because the cooling fan relay was faulty and the cooling fan would not stop. I replaced the fan relay, but noticed the cooling fan still does not stop. I take out the relay and the fan stops. I put the relay in and the fan starts regardless if the car is hot or cold. What could be causing the cooling fan to not turn off? And what do I need to replace to make it work? I have no problems with a dead battery as long as I remove the relay while the car is parked for extended periods of time.