A study is made of the lateral tunneling between edge channels at the depletion-induced edges of a gated two-dimensional electron system, through a gate-voltage-controlled barrier arising when the donor layer of the heterostructure is partly removed along a fine strip by means of an atomic force microscope. For a sufficiently high barrier the typical current-voltage characteristic is found to be strongly asymmetric, having, in addition to the positive tunneling branch, a negative branch that corresponds to the current overflowing the barrier. It is established that the barrier height depends linearly on both the gate voltage and the magnetic field, and the data are described in terms of electron tunneling between the outermost edge channels.