Summary  In the context of a mechanical theory of a Cosserat point developed by Green and Naghdi [1=Quart. J. Mech. and Appl. Math.,44, 335–355 (1991)], this paper establishes a properly invariant theory for infinitesimal deformations. The invariant theory is valid for an elastic Cosserat point with an arbitrary number of directors. Its construction is based on a method developed by Casey and Naghdi [2=Arch. Rational Mech. Anal.,76, 355–391 (1981)] for unconstrained non-polar elastic bodies.