Although the commonly used quadratic Hebbian–anti-Hebbian rules lead to successful models of plasticity and learning, they are inconsistent with neurophysiology. Other rules, more physiologically plausible, fail to specify the biological mechanism of bidirectionality and the biological mechanism that prevents synapses from changing from excitatory to inhibitory, and vice versa. We developed a synaptic bidirectional Hebbian rule that does not suffer from these problems. This rule was compared with physiological homosynaptic conditions in the hippocampus, with the results indicating the consistency of this rule with long-term potentiation (LTP) and long-term depression (LTD) phenomenologies. The phenomenologies considered included the reversible dynamics of LTP and LTD and the effects of N-methyl-D-aspartate blockers and phosphatase inhibitors.