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In this work we report the synthesis and structural, electronic and magnetic properties of La1.5Ca0.5CoMnO6 double-perovskite. This is a re-entrant spin cluster material which exhibits a non-negligible negative exchange bias effect when it is cooled in zero magnetic field from an unmagnetized state down to low temperature. X-ray powder diffraction, X-ray photoelectron spectroscopy and magnetometry results indicate mixed valence state at Co site, leading to competing magnetic phases and uncompensated spins at the magnetic interfaces. We compare the results for this Ca-doped material with those reported for the resemblant compound La1.5Sr0.5CoMnO6, and discuss the much smaller spontaneous exchange bias effect observed for the former in terms of its structural and magnetic particularities. For La1.5Ca0.5CoMnO6, when successive magnetization loops are carried, the spontaneous exchange bias field inverts its sign from negative to positive from the first to the second measurement. We discuss this behavior based on the disorder at the magnetic interfaces, related to the presence of a glassy phase. This compound also exhibits a large conventional exchange bias, for which there is no sign inversion of the exchange bias field for consecutive cycles.