We have measured the Sunyaev-Zeldovich effect towards the Coma cluster ( A1656 ) with the MITO experiment , a 2.6-m telescope equipped with a 4-channel 17 arcminute ( FWHM ) photometer . Measurements at frequency bands 143 \pm 15 , 214 \pm 15 , 272 \pm 16 and 353 \pm 13 GHz , were made during 120 drift scans of Coma . We describe the observations and data analysis that involved extraction of the SZ signal by employing a spatial and spectral de-correlation scheme to remove a dominant atmospheric component . The deduced values of the thermal SZ effect in the first three bands are \Delta T _ { 0 } = - 179 \pm 38 , - 33 \pm 81,170 \pm 35 \mu K in the cluster center . The corresponding optical depth , \tau = ( 4.1 \pm 0.9 ) \times 10 ^ { -3 } , is consistent ( within errors ) with both the value from a previous low frequency SZ measurement , and the value predicted from the X-ray deduced gas parameters .