A search dedicated to the identification of new, dwarf and cold stars close to the Sun has allowed us to measure the radial velocities of a set of stars of late spectral type. The stars selected were M-type stars present in the Hipparcos Input Catalogue located in a strip of +/-20° around the Ecliptic and observables from La Silla. Our inal set contains 22 M-type stars whose radial velocities Vr have been measured with an accuracy of ~ 0.5 km s-1 during a single observing run. From their velocities, parallaxes and magnitudes we deduce that all the stars observed are red giants, with space velocities relative to the Sun mostly lower than 100 km s-1. Based on observations collected at the CAT telescope, European Southern Observatory, La Silla, Chile.