Transmission Mystery Noise

I am driving a 1991 Honda Civic with 245k miles. It is in pretty good mechanical condition except for thing. When I leave the house in the morning it takes a few miles before it will shift from second to third. I will drive along in second with high rpms until it decides to go into third. It makes a scratchy squeal sound for about 1 second when it shifts into third. After that it won’t happen again. Once it is warmed up the transmission seems to function just fine. I changed the transmission fluid and it was not burned or too discolored. That did not seem to help. I don’t want to replace the transmission because of the age of the car if I can help it. Please help.