Context : The variability of the Wolf-Rayet star EZ CMa has been documented for close to half a century , and a clear periodicity of \sim 3.7 days is established .
However , all attempts to prove that it is a binary have failed because the photometric , spectroscopic , and polarimetric variations are not coherent over more than a few orbital cycles .

Aims : In this letter we show that the lack of coherence in the variability can be explained with a very rapid apsidal motion in a binary orbit .

Methods : We measured the times of minima in a recently published exceptionally long photometric light curve obtained by the Toronto BRITE satellite .
The apsidal motion and the system eccentricity are determined from the length of the time intervals between these minima , which alternate in their duration , following a pattern that is clearly associated with apsidal motion .
These minima are superposed on brightness enhancements of the emission from a shock zone , which occur at about the times of periastron phases .

Results : We determine the orbital periodicity , P _ { a } = 3.63 d , and the period of the apsidal motion , U \simeq 100 d , which together yield an average sidereal period of P _ { s } = 3.77 d. The eccentricity is found to be close to 0.1 .
The rate of periapsis retreat changes significantly over the period of observation and is determined to be -16 ^ { \circ } \mathrm { P } ^ { -1 } _ { a } at the beginning of the observing period and -10 ^ { \circ } \mathrm { P } ^ { -1 } _ { a } at the end .

Conclusions : We demonstrate that by introducing a fast apsidal motion , the basic photometric variability is very well explained .
The binary nature of EZ CMa is now established .
This might imply that other apparently single Wolf-Rayet stars that emit hard X-rays , similar to EZ CMa , are also binaries .