We present the results of a search for second generation
leptoquarks S_2 using 19.3 pb^-1 of data collected at the Collider Detector at
Fermilab (CDF) in ppbar collisions at sqrt s = 1.8 TeV during the 1992-93
collider run.  We have searched for S_2 S-bar_2 pairs assuming that each
leptoquark decays to a muon + quark with a branching ratio Beta.  We find two
candidate events, consistent with an expected background of 1.11 +/- 0.48.  We
obtain upper limits on sigma(ppbar -> S_2 S-bar_2) Beta^2 as a function of
M_S_2.  Using a Monte Carlo prediction for S_2 S-bar_2 pair production, we
exclude M_S_2 < 131 GeV/c^2 for Beta = 1 and M_S_2 < 96 GeV/c^2 for Beta = 0.5
at 95% C.L.