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We have obtained radial velocities of the components of the short-period subsystem of the B-type triple star 64 Orionis, covering a full cycle of the long-period orbit since the date of our earlier paper by Fekel & Scarfe. We use all of our radial velocities, together with available speckle interferometry, to derive a three-dimensional orbit for the long-period system. The system has orbital periods of 14.57213 days and 12.98 yr. We also determine spectroscopically a magnitude difference at 4500 Å of 1.0 ± 0.1 between the components of the close pair. Although radial velocities of the third component continue to elude us, we are able to derive masses and luminosities for all three components by requiring that they lie within the populated band of the observed mass-luminosity relationship. With this constraint, the orbital parallax is 0farcs00374 ± 0farcs00017. Our results are consistent with the spectral types and colors derived previously and with the b magnitude difference determined by earlier lunar occultation observations, within the uncertainties of those parameters.