The stability of closed shell bimetallic magic clusters MAu(4) (M=Ti and Zr) is investigated theoretically through ab initio molecular orbital calculations. Both these clusters have tetrahedral structures and are found to be associated with large values of the ionization potential, HOMO-LUMO gap as well as the binding energies, which are characteristic of the magic clusters. However, the cluster-cluster interaction energy corresponding to a dimer formation is found to be unusually high ( approximately 5-7 eV) in contradiction to the usual properties of a magic cluster and is attributed to a 3-center-2-electron M-Au-M type bridge bonding as well as aurophilic attraction. Gross geometrical features of the individual clusters are, however, mostly retained in the dimer, thus satisfying the basic requirements for the cluster-assembled materials. This work would have important implications in the design of novel cluster-based nanomaterials for various nanoscale applications.