In a previous study [R. J. Harrison , J. Chem. Phys. (in press)] we reported an efficient, accurate multiresolution solver for the Kohn-Sham self-consisitent field (KS-SCF) method for general polyatomic molecules. This study presents an efficient numerical algorithm to evalute Hartree-Fock (HF) exchange in the multiresolution SCF method to solve the HF equations. The algorithm employs fast integral convolution with the Poission kernel in the nonstandard form, screening the sparse multiwavelet representation to compute results of the integral operator only where required by the nonlocal exchange operator. Localized molecular obitals are used to attain near linear scaling. Results for atoms and molecules demonstrate reliable precision and speed. Calculations for small water clusters demonstrate a total cost to compute the HF exchange potential for all n(occ) occpuied MOs scaling as O(n(occ)(1.5)). (C) 2004 American Institute of Physics.