The Ruderman-Kittel-Kasuya-Yosida (RKKY) indirect-exchange interaction via free carriers is analyzed in the case of IV-VI semimagnetic semiconductors (diluted magnetic semiconductors). Carriers responsible for the RKKY interaction in these materials originate from the anisotropic band of heavy holes located at the point of the Brillouin zone (i.e., there are 12 equivalent valleys of this band). Both intervalley and intravalley electron processes contribute to the exchange coupling. Calculations of the RKKY exchange integral and the paramagnetic Curie temperature (FTHETA) are presented. The exchange integral is anisotropic, and its dependence on the interspin distance is significantly modified in such a way that the role of antiferromagnetic couplings is increased. As a consequence, the value of FTHETA is reduced.