This paper shows that angular distribution of spin-unresolved Auger electrons emitted in the decay of a vacancy created by the absorption of a photon in a certain class of free, unpolarized and gaseous non-linear molecules is completely characterized by three, rather than by two well-known parameters. The presence of this additional third parameter gives rise to circular dichroic effect which varies as cosine of the angle made by the departing Auger electron with the direction of incidence of the circularly polarized radiation. Linear dichroic effect varies as the square of sine of the angle made by the direction of emission of Auger electron and the polar axis of the space frame. Linear and circular dichroism in the angular correlation between theE₁ photoelectron and Auger electron emitted sequentially from a molecule belonging to one of the 32 point groups has also been investigated.