Observations from the first flight of the Medium Scale Anisotropy Measurement (MSAM1-92) are analyzed to search for the Sunyaev-Zeldovich (SZ) effect towards the Coma cluster. This balloon-borne instrument uses a $28arcmin$ FWHM beam and a three position chopping pattern with a throw of $pm40arcmin$. With spectral channels at 5.7, 9.3, 16.5, and 22.6~icm, the observations simultaneously sample the frequency range where the SZ spectral distortion in the intensity transitions from a decrement to an increment and where the fractional intensity change is substantially larger than in the Rayleigh-Jeans region. We set limits on the Comptonization parameter integrated over our antenna pattern, $Delta y leq 8.0 times 10^{-5}$($2 sigma$). For a spherically symmetric isothermal model, this implies a central Comptonization parameter, $y_o leq 2.0 times 10^{-4}$, or a central electron density, $n_o leq 5.8 times10^{-3}$cm$^{-3}h_{50}$, a result consistent with central densities implied by X-ray brightness measurements and central Comptonization estimates from lower frequency observations of the SZ effect.
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