We report on the study and successful application of an improved measurement method for solar flares at millimeter wavelengths. A 210 GHz multibeam receiver for the observation of solar bursts was installed in the KOSMA 3 m telescope on the Gornergrat. It consists of three radiometer channels, with a fourth beam synthesised from the other three. The four inter- secting beams allow measurements of source locations with arcsecond resolution and, for the first time, also the determination of the effective source size at short millimeter waves. The typical sensitivity of <1.5 sfu allows also the detection of weak flares at millisecond time resolution. In this paper we present the instrument and the numerical method for the determination of the source flux density, position and effective size, as well as simulations to asses the validity of the method. First observational results were obtained for the GOES X17.2 flare on October 28, 2003. The event reached a peak flux density of 11 000 sfu at 210 GHz and exhibited a slowly varying, time-extended emission from an extended source (effective diameter ≈ 60 arcsec), as well as a short-lived component from a compact source (<10 arcsec) originating from a different location.