We report on the thermoelectric power S(T), electrical resistivity and thermal conductivity measurements on the antiferromagnetic CeCoAl4 compound and on the nonmagnetic reference compound, LaCoAl4. The Néel temperature of CeCoAl4 is T[Formula: see text] = 13.5 K and a metamagnetic-like transition occurs in the magnetic field of about 7.5 T. We show that the magnetic contribution to the thermoelectric power, S[Formula: see text](T), exhibits a large peak due to the crystal electric field (CEF) at about 240 K and a small anomaly around the ordering temperature. Surprisingly, the CEF related S[Formula: see text](T) peak is close to the upper CEF excitation energy [Formula: see text] = 202 K, in contrast to the usual case of the peak position being located at a fraction of the observed CEF energy level. The applicability of different theoretical and phenomenological models describing the temperature dependence of the Seebeck effect S[Formula: see text](T) has been tested and finally a calculation is proposed, which incorporates a full CEF levels scheme.