  The bright WN4 star EZ CMa exhibits a 3.77 day periodicity in photometry,
spectroscopy, and polarimetry but the variations in the measurements are not
strictly phase-locked, exhibiting changes in reference times, amplitudes, and
the shape of the variability happening over times as short as a few weeks.
Recently, 137 days of contiguous, variable photometry from BRITE-Constellation
was interpreted as caused either by large-scale dense wind structures modulated
by rotation, or by a fast-precessing binary having a slightly shorter 3.626 day
orbital period and a fast apsidal motion rate of $1315^\circ\,\text{yr}^{-1}$.
We aim at testing the latter hypothesis through analysis of spectroscopy and
focus on the N\,{\sc v} $\lambda\,4945$ line. We derive an orbital solution for
the system and reject the 3.626 day period to represent the variations in the
radial velocities of EZ CMa. An orbital solution with an orbital period of 3.77
days was obtained but at the cost of an extremely high and thus improbable
apsidal motion rate. Our best orbital solution yields a period of
$3.751\pm0.001$\,days with no apsidal motion. We place our results in the
context of other variability studies and system properties. While we cannot
fully reject the precessing binary model, we find that the corotating
interaction region (CIR) hypothesis is better supported by these and other data
through qualitative models of CIRs.
