A class of two‐dimensional force‐free equilibria are shown to be subject to an ideal linear instability. This instability is similar to the coalescence instability for chains of magnetic islands. Semianalytic methods are used to find second magnetic equilibrium which is accessible from the first and has lower magnetic energy. This equilibrium has a discontinuous magnetic field and current sheets at these discontinuities. Numerical simulations indicate that the nonlinear evolution of the instability allows the plasma to relax to this discontinuous equilibrium.