Two‐dimensional dissipative magnetohydrodynamic turbulence is randomly driven at small spatial scales and is studied by numerical simulation in the presence of a strong uniform external magnetic field. A novel behavior is observed which is apparently distinct from the inverse cascade that prevails in the absence of an external magnetic field. The magnetic spectrum becomes dominated by the three longest‐wavelength Alfve´n waves in the system allowed by the boundary conditions: those which, in a box size of edge 2&pgr;, have wavenumbers (kx,ky) =(1,0),(1,1), and (1,−1), where the external magnetic field is in thexdirection. At any given instant, one of these three modes dominates the vector potential spectrum, but they do not constitute a resonantly coupled triad. Rather, they are apparently coupled by the smaller‐scale turbulence.