We consider, in this paper, a vector field in Space-time $\mathrm V_4$, which is steady in the relativistic sense, i.e. which does not depend on a timelike parameter. This means that there exists, in every point of $\mathrm V_4$, a frame such that corresponding vector of the field considered is steady with respect to its proper time. We choose this frame among those which see considered vector in its „original" length, i.e. which perform motions locally orthogonal to it. So we obtain a property of that kind of frames, to have either Born's rigidity, in the direction parallel to the vector considered, or to move geodesically.