The structural parameters, chemical bonding and magnetic properties of the ternary boride series M1.5Rh5.5B3 (M = Cr, Mn, Fe, Co, Ni) were investigated by first principles DFT calculations. The calculated crystallographic lattice parameters corroborate well with the experimental results of the reported Fe1.3Rh5.7B3 single crystal. In the most stable structural model used, Fe-dumbbells as well as isolated Fe-atoms exist. From spin polarised calculations, ferromagnetism is found for the members with M = Fe, Co, while ferrimagnetism is more stable for Mn1.5Rh5.5B3 and Pauli paramagnetism is more stable for M = Cr, Ni. The total magnetic moment per formula unit for the M = Mn, Fe and Co phases is calculated to be 3.32, 5.00 and 3.26 μB, respectively. According to COHP chemical bonding analysis, Rh-B contacts are mainly responsible for the structural stability, while Rh-M interactions influence the magnetic behavior of these complex borides. [ABSTRACT FROM AUTHOR]