  We analytically calculate the contribution of transverse momentum
conservation to the azimuthal correlations that have been proposed as signals
for possible local strong parity violation and recently measured in heavy ion
collisions. These corrections are of the order of the inverse of the total
final state particle multiplicity and thus are of the same order as the
observed signal. The corrections contribute with the same sign to both
like-sign and opposite-sign pair correlations. Their dependence on the momentum
is in qualitative agreement with the measurements by the STAR collaboration,
while the pseudorapidity dependence differs from the data.
