The main features of the four-alpha-helix bundle, one of the characteristic structural elements of many proteins, can be explained in terms of noncovalent interactions between the constituent helices. Conformational energy computations have been carried out on four types of four-alpha-helix bundles, each consisting of four CH3CO-(L-Ala)10-NHCH3 polypeptide chains, with various combinations of parallel and antiparallel orientations of the helices. In the bundle with the most favorable energy, all pairs of neighboring helices are oriented antiparallel--i.e., in the orientation that is favored by electrostatic interactions between the helices. In this structure, the orientation angle between neighboring helix axes is -168 degrees, within +/- 7 degrees, in close agreement with the orientation angles observed in proteins and with the value that we computed earlier for the most favorable packing of pairs of interacting alpha-helices. This orientation corresponds to a left-handed twisting of the helical bundle. The preferred handedness of this twisting arises as a result of favorable nonbonded interactions between the alpha-helices.