The authors wish to acknowledge the support of the United States Department of Energy, Office of Basic Energy Sciences, under grant No. DE-FG02-85ER45203. Critical review by Professor Dorian Hatch of the Physics Department at Brigham Young University is gratefully acknowledged. A new asymmetric domain for intercrystalline misorientation is defined in the space of Euler angles for materials exhibiting cubic (Oh point-group) lattice symmetry. The invariant measure for this new domain is nearly constant; this is in significant contrast to the previous domain defined by MacKenzie [Biornetrika (1958), 45, 229-240]. Distribution functions in the misorientation can now be represented with greater clarity and convenience in the new domain. A detailed theoretical analysis of special misorientations exhibiting multiplicities m > 1 is described. It is demonstrated that all such special misorientations fall upon the surfaces separating distinct asymmetric domains. This result convincingly proves that the derived asymmetric domain is correct. The location of all possible coincidence site lattice boundaries for E <= 49 are identified in the asymmetric domain, and their characteristic multiplicities are given.