A new mechanism for slow light is introduced by employing a symmetrical metal-cladding optical waveguide with millimeter scale. The basis is the anomalous dispersion of the ultrahigh-order modes near zero wavenumber, where the effective index approaches zero. Without use of any coherent or material resonance, this scheme is not subject to limitations of the delay-bandwidth product and can generate arbitrarily small group velocities over an unusually large frequency bandwidth.