A new corotational procedure is developed which enables existing finite element formulations to be used in problems that contain arbitrarily large rotations. Through the use of a nonsingular large rotation vector, the contribution of the rigid body motion of the element to the total displacement field is removed before element computations are performed, with the result that almost any element can be easily upgraded to handle large rotations. This paper contains a derivation of the theory, an outline of the implementation into the STAGS code, and a demonstration of performance for problems involving large rotations and moderate strains.