Observations from the first flight of the Medium Scale Anisotropy Measurement (MSAM1-92) are analyzed to search for the Sunyaev-Zel'dovich (SZ) effect towards the Coma cluster. This balloon-borne instrument uses a 28 ′ FWHM beam and a three position chopping pattern with a throw of ±40 ′ . With spectral channels at 5.7, 9.3, 16.5, and 22.6 cm −1 , 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, ∆y ≤ 8.0 × 10 −5 (2σ). For a spherically symmetric isothermal model, this implies a central Comptonization parameter, y o ≤ 2.0 × 10 −4 , or a central electron density, n o ≤ 5.8 × 10 −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.