Transferring schools on F1

[Samputta1978]

Hi, 

I am coming to states in August on F1  for a short summer course which lasts for 4 weeks and my F1 has a validity of 4 weeks. After finishing my course i am thinking to join a  Masters program which starts in October. My question is do i need to go back to my country and apply for F1 again or i can transfer my sevis record to the new university within the 60 days grace period after the course. I even hold a valid b1b2 visa.