  We construct a covariant quantum superstring, extending Berkovits' approach
by introducing new ghosts to relax the pure spinor constraints. The central
charge of the underlying Kac-Moody algebra, which would lead to an anomaly in
the BRST charge, is treated as a new generator with a new b-c system. We
construct a nilpotent BRST current, an anomalous ghost current and an
anomaly-free energy-momentum tensor. For open superstrings, we find the correct
massless spectrum. In addition, we construct a Lorentz invariant B-field to be
used for the computation of the integrated vertex operators and amplitudes.
