  The complete absence of radio pulsars with periods exceeding a few seconds
has lead to the popular notion of the existence of a high $P$ death line. In
the standard picture, beyond this boundary, pulsars with low spin rates cannot
accelerate particles above the stellar surface to high enough energies to
initiated pair cascades through curvature radiation, and the pair creation
needed for radio emission is strongly suppressed. In this paper we postulate
the existence of another pulsar ``death line,'' corresponding to high magnetic
fields $B$ in the upper portion of the $\dot{P}$--$P$ diagram, a domain where
few radio pulsars are observed. The origin of this high $B$ boundary, which
occurs when $B$ becomes comparable to or exceeds $10^{13}$ Gauss, is again due
to the suppression of magnetic pair creation $\gamma\to e^+e^-$, but in this
instance, primarily because of ineffective competition with the exotic QED
process of magnetic photon splitting. This paper describes the origin, shape
and position of the new ``death line,'' above which pulsars are expected to be
radio quiet, but perhaps still X-ray and $\gamma$-ray bright.
