An exact solution for the magnetohydrodynamic equations for a time‐dependent, two‐dimensional flow of an incompressible plasma of finite conductivity in a hyperbolic magnetic field is given. This solution admits a nonzero initial current density, and predicts a sequence of events associated with the evolution of a current sheet in a plasma subjected to an initial hyperbolic magnetic field configuration. This is confirmed by laboratory experiments. Next, the calculation is extended to include the density variations in the plasma. The corresponding solution predicts that the current sheet at the neutral point evolves more rapidly when the plasma density builds up locally around the magnetic neutral point.