Mumford proved that psi(g)-lambda(1)psi(g-1)+...+(-)(g)lambda(g) = 0 in the Chow ring of (M) over bar (g,1). We find an explicit recursive formula for psi(g) - lambda(1)psi(g-1)+...+(-1)(g)lambda(g) in the tautological ring of (M) over bar (g,1) as a combination of classes Supported on boundary strata.