If you wish to transfer to another institution while studying on an F-1 student visa, you will need to be a full time student and in good academic standing. You will also need to insure that the school you are transferring to is approved by USCIS to educate Foreign Students.
Even if you have completed or been terminated from a school, that school is still obligated to transfer your SEVIS record to any school you desire. If your current/previous school refuses to transfer your SEVIS record, work with the DSO at your new school to try to resolve the situation. A school cannot refuse to transfer SEVIS records for any financial or business reasons.