The electronic structure and magnetic properties of rhodium clusters with sizes of one to 43 atoms embedded in a nickel host are studied by first-principles spin-polarized calculations within the local density functional formalism. A single Rh atom in Ni matrix is found to have a magnetic moment of 0.45 mu B. Rh₁₃ and Rh₁₉ clusters in Ni matrix have lower magnetic moments compared with the free ones. The most interesting finding is that Rh₄₃ cluster, which is bulk-like and non-magnetic in vacuum, becomes ferromagnetic when embedded in the nickel host.