We propose a simple new configuration of measurements for the detection of gravitational waves using a Weber-type gravitational wave antenna. The detection scheme is characterized by three normal modes of vibration; one of them is uncoupled to the gravitational wave interaction, and it is available as an anticoincidence veto for signals of different origin, such as those due to cosmic rays interacting with the antenna. Moreover, on the basis of a simplified analysis of the signal-to-noise ratio of this setup, we show that it is easier to approach the final sensitivity limit of a linear detection scheme of measurements.