  In a joint paper P. Pand\v{z}i\'c and D. Renard proved that holomorphic and
antiholomorphic discrete series representations can be constructed via
algebraic Dirac induction. The group $SU(2,1)$, except for those two types,
also has a third type of discrete series representations that are neither
holomorphic nor antiholomorphic. In this paper we show that nonholomorphic
discrete series representations of the group $SU(2,1)$ can also be constructed
using algebraic Dirac induction.
