From there, he would go to Mississippi State, where his team would battle Kentucky (a team that went on to win the NCAA championship) to the wire on national television.
"They rarely took more than one team from each conference then," Greene said. "But we were good enough to win the national championship that year, too."
Then it was time to come home.
"Marshall Gordon, the vice president for university relations at Murray State, asked me if there were any coaches I could recommend for them," Greene said. "I gave him a couple of names, and he said he didn't expect I'd be interested in discussing the job.
“Well, I said since it was my alma mater I'd be willing to listen. But I was really just being courteous. So we got together and he asked me what it would take for me to come to Murray State, and I outlined about 15 or 20 things. At breakfast the next morning, he said it was done and asked me to come and take a look."
Greene did just that. After meeting everyone and touring the campus, his mind was made up. He was going to say no. But before he could, Gordon asked him to sleep on it first.
Around 3:30 or 4 in the morning, Greene changed his mind.
"My alma mater needed me and I answered the call," he said. "It probably hadn't happened before or since, a coach leaving an SEC school for an OVC school.
"I took my son, David, to visit the campus at Mississippi State, and he said he couldn't understand why I left. I asked him if he thought I had rocks in my head, and he told me he thought they were boulders."
While at Murray State, Greene took a program on the brink of collapse - a program with three OVC titles in its history - and led it to three conference championships in six years.
It didn't come easy, though. The Racers were a dismal 4-22 his first year. At Christmas time of that year, The Murray State News ran a story headlined "The Hanging of Greene."
"We completely turned the roster upside down," he recalled. "But we beat Western twice that year. Our second year, we went 23-8. That was the biggest turnaround in the history of the NCAA at the time."
Of course, no coach can be successful without great players. And Greene excelled at finding them, sometimes by spotting greatness in players others didn't want.
Lamont Sleets and Glen Green are prime examples of his recruiting acumen.
"A lot of people looked at Sleets and said, 'He's not a very good point guard because he doesn't handle the ball very well,'" Greene recalled. "But he played forward for Eminence High School. He was a 5-9 forward, but he was the best dunker I ever had. He could jump up and do a 180 and jam it.
"He was like Calvin Murphy. He could take one step beyond the circle at mid-court and jump up and bomb it. He was physical, too - a strong kid and a very good player. Glen Green was 6-7 and thin. Ole Miss said he was too skinny and wouldn't be able to handle the beating in the SEC. Fine. We put Sleets at two-guard and Glen at the point. That gave us a 6-7 point guard and a 5-9 two-guard. It's all about putting the right people in the right places."