  We have investigated the invariant mass spectrum of dimuons collected by the
CDF experiment during the 1992-1995 run of the Fermilab Tevatron collider to
improve the limit on the existence of narrow resonances set by the experiments
at the SPEAR e+e- collider. In the mass range 6.3-9.0 GeV/c^2, we derive 90%
upper credible limits to the ratio of the production cross section times muonic
branching fraction of possible narrow resonances to that of the Y(1S) meson. In
this mass range, the average limit varies from 1.7 to 0.5%. This limit is much
worse at the mass of 7.2 GeV/c^2 due to an excess of 250+-61 events with a
width consistent with the detector resolution.
