A proper Frenet tetrad is associated with each point of the world-line of a classical point particle. It is shown that this is equivalent to the introduction of a unimodular 2×2 matrix (or, correspondingly, a suitably normed 4-spinor) as a function of the proper time, this «proper 4-spinor» being determined by the Lorentz transformation which transforms a fixed set of Cartesian axes into the proper tetrad at the point considered. The rate of change of the proper 4-spinor as the particle moves along the world-line is given by a spinor equation which involves the three curvatures and is entirely equivalent to the Frenet formulae. The proper 4-spinor is determined for simple types of worldlines. In particular, it is shown that in the case of 4-dimensional helices for which the third curvature vanishes and the other two curvatures remain constant, one obtains the world-line of a free spinning particle as described byWeyssenhoff while the proper 4-spinor attached to such a particle satisfies the classical analogue of Dirac’s equation recently postulated byProca.