It will depend on the school. For many schools it is part of their accreditation criteria that they cannot accept MS students who have not completed a four year

It will depend on the school. For many schools it is part of their accreditation criteria that they cannot accept MS students who have not completed a four year bachelor program. This was true for instance when I went to Georgia Tech—often to the frustration of international students who had a three year degree that their home country considered equivalent to a four year program. So it will depend on the criteria for each school, but it is probably most common in the US that you must have a regionally accredited undergraduate degree before starting a graduate program at a major university.