A measurement of the N*--N* ++ mass and width differences is described, where N* is the nucleon resonance with i"(/ p )=f(l + ) and mass approximately 1240 MeV. The resonances were produced in the inelastic reactions nn-* p mC and p p ->n p ir + , which are known to proceed almost entirely via N*~ and N* ++ production, respectively, in the observed energy region. A comparison of the (mr~) and (pir + ) effectivemass distributions gives a mass difference of 7.9±6.8 MeV and a width difference of 25±23 MeV for iV*-N* ++ . This result agrees with predictions based on the SU (3) and SU(6) symmetry schemes.