The interchange instability is studied in an equilibrium similar to that of a stellarator with helical windings, on the basis of the combined Maxwell and Vlasov equations in the limit of small particle gyration radii. However, the first correction in the size of these radii and its effect on the stability criterion is studied. It is found that, just as in the work of Rosenbluth, Krall, and Rostoker, the stability criterion may be expressed in terms of the growth ratesHof the zero‐gyration‐radius theory. The stability is always improved by this correction and the new stability criterion is given bysH/&OHgr; <ma2/R2, where &OHgr; is the ion gyration frequency,athe ion gyration radius,Rthe radius of the plasma, andmthe azimuthal wavenumber. The zero‐gyration‐radius normal mode equation and growth rates are then found and these are applied to the special case of helical windings with trefoil symmetry. It is shown that even when the gyration radius is small its effect may be significant, in many cases increasing the plasma pressure which may be stably confined by a factor of 2 or more.