This paper studies the possibility of building a Modular Multilevel Converter (M2C) using Silicon Carbide (SiC) switches. The main focus is on a theoretical investigation of the conduction losses of such a converter and a comparison to a corresponding converter with silicon insulated gate bipolar transistors. Both SiC BJTs and JFETs are considered and compared in order to choose the most suitable technology. One of the sub-modules of a down-scaled 10 kVA prototype M2C is replaced with a sub-module with SiC JFETs without anti-parallel diodes. It is shown that diode-less operation is possible with the JFETs conducting in the negative direction, leaving the possibility to use the body diode during the switching transients. Experimental waveforms for the SiC sub-module verify the feasibility during normal steady-state operation. The loss estimation shows that a 300 MW M2C for high-voltage direct current transmission would potentially have an efficiency of approximately 99,8 % if equipped with future 3.3 kV 1.2 kA SiC JFETs.