The magnetic properties of small AgnTM clusters (n = 3-7, 12; TM = Ru, Rh, Pd) have been studied using a linear combination of atomic orbitals approach with the density functional formalism, and the Kohn-Sham equation is solved self-consistently with the discrete variational method (DVM). The symmetry-quenching effect is found that the magnetic moments of Rh in D 3 h structure and Ru in T d structure are quenched to zero. Meanwhile, it is found that Ru and Rh are magnetic (except for symmetry-quenching), and Pd is nearly nonmagnetic. The effects of symmetry, coordination number and atomic distance on the magnetic moment of 4d impurities are discussed.