Recent experiment on the mass spectrum of ZnO clusters revealed a (ZnO) 34 magic cluster with enhanced stability [A. Dmytruk, et al., Microelect. J. 40 (2009) 218]. We have performed an extensive search for the most stable structure of (ZnO) 34 using gradient-corrected density-functional theory. Instead of the previously nominated onion-like nested cage of (ZnO) 6 @(ZnO) 28 , we found that the hollow cage structures satisfying the isolated six square rule constitute the most preferred structural motif for (ZnO) 34 cluster.