We examine a premixed flame located in a plane counterflow of fresh cold mixture and hot inert. The temperature of the inert is significantly less than the adiabatic flame temperature so that the name response to strain-rate variations is multivalued for a finite interval of strain rates. In this interval there are two stable one-dimensional solutions, one characterized by vigorous combustion, the ether by weak combustion. Numerical solutions are constructed that describe an unsteady two-dimensional evolution between the two solutions in the direction normal to the straining-now plane. Following an initial transient, this evolution consists of a wave of permanent form, traveling at constant speed in the out-of-plane direction. This wave is an edge-flame whose speed is positive or negative, depending on the value of the strain rate. The role of edge-names in the failure of upward rising methane/air names in sublimit mixtures is briefly discussed.