We propose a mechanism for the formation of multiple bands at an ice edge that is subjected to an off-ice wind. The wind moves the outermost floes seaward faster than the interior ice, dilating the marginal ice zone and opening up random polynyas. In the largest of the polynyas, the off-ice wind generates a significant fetch-limited wave spectrum, which produces a wave radiation pressure on floes at the downwind end of the polynya, increasing their velocity. They are herded against their downwind neighbors, creating a band of high ice concentration. The band is stabilized by an internal compacting stress due to the exponential decay of the wind-wave spectrum across the band and to a slower decay of swell incident from seaward. The band's growth terminates when it encounters a second downwind polynya of sufficiently large size. We show how an array of 'immature' bands generated in this way 'mature' by selective mergers into larger, regularly spaced bands of approximately equal width.