  The cyclotron line in the spectrum of the accretion-powered pulsar Her X-1
offers an opportunity to assess the ability of the BATSE Spectroscopy Detectors
(SDs) to detect lines like those seen in some GRBs. Preliminary analysis of an
initial SD pulsar mode observation of Her X-1 indicated a cyclotron line at an
energy of approximately 44 keV, rather than at the expected energy of
approximately 36 keV. Our analysis of four SD pulsar mode observations of Her
X-1 made during high-states of its 35 day cycle confirms this result. We
consider a number of phenomenological models for the continuum spectrum and the
cyclotron line. This ensures that we use the simplest models that adequately
describe the data, and that our results are robust. We find modest evidence
(significance Q ~ 10^-4-10^-2) for a line at approximately 44 keV in the data
of the first observation. Joint fits to the four observations provide stronger
evidence (Q ~ 10^-7-10^-4) for the line. Such a shift in the cyclotron line
energy of an accretion-powered pulsar is unprecedented.
