A rotary hinge for an electronic device with a cover and a body is mounted between a bottom of the cover and a top of the body and has a receiving assembly, a connecting assembly and a retaining assembly. The receiving assembly is connected to the cover. The connecting assembly is connected to the body and is attached pivotally to the receiving assembly. The retaining assembly is connected respectively to the receiving and connecting assemblies to selectively hold the cover at closed and open positions. With only one pivot between the rotary hinge and the cover, part of the body is exposed to allow the input unit being used when the cover is pivoted to open. Regardless of opening or closing the cover, the rotary hinge is hidden to prevent from damaging and foreign matters.