We present fur the first time the results of very high Q factor measurements for a 2.8 Erg fused silica mass suspended by two fused quartz fibers attached by a novel technique for joining fused silica or quartz. The Q for the pendulum mode at 0.93 Hz was (2.3 +/- 0.2) x 10(7), the highest value demonstrated to date for a mass of this size; By employing such a new suspension system the sensitivity of the gravitational wave detectors currently under construction can be increased up to 1 order of magnitude.