Recent works in modified compressed sensing (CS) show that reconstruction of sparse or compressible signals with partially known support yields better results than traditional CS. In this paper, we extend the ideas of these works to modify the iterative hard thresholding (IHT) algorithm to incorporate known support in the recovery process. We present a theoretical analysis that shows that including prior support information relaxes the conditions for stable reconstruction. Numerical results show that the IHT modification improves performance, thereby needing fewer samples to yield an approximate reconstruction.