  A new method is presented for determining event-by-event fluctuations of
elliptic flow, $v_2$, using first-order event planes. By studying the
event-by-event distributions of $v_2$ observables and first-order event-plane
observables, average flow $\avg{v_2}$ and event-by-event flow fluctuations can
be separately determined, making appropriate allowance for the effects of
finite multiplicity and non-flow. The method has been tested with Monte Carlo
simulations. The connection between flow fluctuations and fluctuations of the
initial-state participant eccentricity is discussed.
