A scheme is proposed for the generation of W entangled states for several atoms trapped in a cavity by detecting photon decay. The scheme works in the regime,where the cavity decay rate is larger than the atom-cavity coupling strength. Thus, the requirement for the quality factor of the cavity is greatly loosened, which is of importance in view of experiment. Another advantage of this schemen is that the atoms are always populated in two ground states coupled by Raman transitions, thus the spontaneous emission can also be suppressed.