  A $b$-ghost was constructed for the $D=11$ non-minimal pure spinor
superparticle by requiring that $\{Q , b\} = T$ where $Q =
\Lambda^{\alpha}D_{\alpha} + R^{\alpha}\bar{W}_{\alpha}$ is the usual
non-minimal pure spinor BRST operator. As was done for the $D=10$ $b$-ghost, we
will show that the $D=11$ $b$-ghost can be simplified by introducing an
$SO(10,1)$ fermionic vector $\bar{\Sigma}^{i}$ constructed out of the fermionic
spinor $D_{\alpha}$ and pure spinor variables. This simplified version will be
shown to satisfy $\{Q, b\} = T$ and $\{b , b\} =$ BRST - trivial.
