Herein is presented a refinement of the theory published by Finn (1999) for the m(theta)=1 diocotron instability. A rigorous definition of the plasma length is introduced and the expression for the velocity field is improved, inasmuch as the effect of the finite size of the plasma column is included. The effect of the perturbation of the plasma length is considered rigorously by using a Green-function approach. A parametric study of the instability for a hollow profile is shown. (C) 2001 American Institute of Physics.