An exact, self‐consistent solution of the system of Vlasov's plus Maxwell's equations is derived, describing a warm stationary plasma in a uniformly sheared magnetic field. It is found that there is no upper limit for the rate of shear; that is, the distance over which the direction of the magnetic field rotates of an angle 2&pgr; can be as small as desired; in particular this distance can be smaller than the ion or even the electron Larmor radius. Within the assumed model, for any value of plasma density, magnetic field strength and rate of sheara prioriassigned, there exists a one‐parameter family of solutions, differing from each other essentially for the fraction of the total current that goes into ion or electron current, respectively. The two currents can also flow in opposite directions, thus subtracting from each other in producing the net total current; in this case, however, they cannot separately exceed certain limiting values, set by the requirement of integrability for the distribution functions.