One distinctive feature of Purkinje cells is that they have two types of discharge: in addition to simple spikes they fire complex spikes in response to input from the climbing fibers. These complex spikes have an initial rapid burst of spikes and spikelets followed by a sustained depolarization; in some models of cerebellar function this climbing fiber input supervises learning in Purkinje cells. On the other hand, synaptic plasticity is often thought to rely on the timing of pre-synaptic and post-synaptic spikes. It is suggested here that the period of depolarization following a complex spike, combined with a simple spike-timing-dependent plasticity rule, gives a mechanism for the climbing fiber to supervise learning in the Purkinje cell. This proposal is illustrated using a simple simulation in which it is seen that the climbing fiber succeeds in supervising the learning.