  We propose a design for the magnetic memory cell which allows an efficient
storage, recording, and readout of information on the basis of thin film
ferromagnetic nanorings. The information bit is represented by the polarity of
a stable 360$^\circ$ domain wall introduced into the ring. Switching between
the two magnetization states is achieved by the current applied to a wire
passing through the ring, whereby the $360^\circ$ domain wall splits into two
charged $180^\circ$ walls, which then move to the opposite extreme of the ring
to recombine into a $360^\circ$ wall of the opposite polarity.
