A proposed rule aimed at restricting the movement of graduate transfer athletes by levying penalties on the colleges that accepted them was voted down on Friday by the N.C.A.A. Division I Council.

The proposal, which applied only to football and men’s and women’s basketball, would have docked teams a scholarship for an additional year if a graduate transfer did not earn his or her secondary degree within one year — even though most graduate degrees take two years to complete. The loss of an additional year’s scholarship was meant to discourage colleges from accepting graduate transfers.

The proposal was put forth last year after 18 months of study by a task force seeking to stem the increase in graduate transfer students, who since 2011 have been able to transfer and play immediately if they have earned their undergraduate degree.

Even though there were about 125 graduate transfers in men’s basketball, they accounted for a small portion — about 3 percent — of all Division I players. But a number of them were prominent. Texas Tech relied on two graduate transfers — Matt Mooney and Tariq Owens — to reach the N.C.A.A. men’s basketball championship game this month.