  Extended BRST invariance (BRST plus anti-BRST invariances) provides in
principle a natural way of introducing the complete gauge fixing structure
associated to a gauge field theory in the minimum representation of the
algebra. However, as it happens in topological Yang Mills theory, not all gauge
fixings can be obtained from a symmetrical extended BRST algebra, where
antighosts belong to the same representation of the Lorentz group of the
corresponding ghosts. We show here that, at non interacting level, a simple
field redefinition makes it possible to start with an extended BRST algebra
with symmetric ghost antighost spectrum and arrive at the gauge fixing action
of topological Yang Mills theory.
