  The magnetic properties of the ferrimagnetic cobaltite CaBaCo$_4$O$_7$ are
systematically investigated. We find that the susceptibility exhibits a
downward deviation below $\sim$ 360 K, suggesting the occurrence of short range
magnetic correlations at temperature well above $T_C$. The effective moment is
determined to be 4.5 $\mu_B$/f.u, which is consistent with that expected for
the Co$^{2+}$/Co$^{3+}$ high spin species. Using a criterion given by Banerjee
[Phys. Lett. \textbf{12}, 16 (1964)], we demonstrate that the paramagnetic to
ferrimagnetic transition in CaBaCo$_4$O$_7$ has a first order character.
