We study the magnetic circular dichroism (MCD) of exciton states near the band edge of CdSe nanocrystallites (quantum dots). The experiment probes the difference between left and right circularly polarized transitions in the presence of an external magnetic field. Analysis of the MCD signal determines the sign and magnitude of the: exciton g-factor which is shown to be highly sensitive to the energy band parameters used in the effective mass approximation, The observation of theoretically predicted changes in The sign of the exciton g-factor between the first two transitions is in agreement with recent theory describing the presence of fine structure underlying the optical transitions of CdSe nanocrystallites.