A bi-directional read/program non-volatile memory cell and array is capable of achieving high density. Each memory cell has two spaced floating gates for storage of charges thereon. The cell has spaced apart source/drain regions with a channel therebetween, with the channel having three portions. One of the floating gate is over a first portion; another floating gate is over a second portion, and a gate electrode controls the conduction of the channel in the third portion between the first and second portions. A control gate is connected to each of the source/drain regions, and is also capacitively coupled to the floating gate. The cell programs by hot channel electron injection, and erases by Fowler-Nordheim tunneling of electrons from the floating gate to the gate electrode. Bi-directional read permits the cell to be programmed to store bits, with one bit in each floating gate.