We present a comprehensive study of Z CVn, an RR Lyrae star that shows long-term cyclic variations of its pulsation period. A possible explanation suggested from the shape of the O-C diagram is the light travel-time effect, which we thoroughly examine. We used original photometric and spectroscopic measurements and investigated the period evolution using available maximum times spanning more than one century. If the binary hypothesis is valid, Z CVn orbits around a black hole with minimal mass of $56.5$ $mathfrak{M}_{odot}$ on a very wide ($P_{rm orbit}=78.3$ years) and eccentric orbit ($e=0.63$). We discuss the probability of a formation of a black hole-RR Lyrae pair and, although we found it possible, there is no observational evidence of the black hole in the direction to Z CVn. However, the main objection against the binary hypothesis is the comparison of the systemic radial velocity curve model and spectroscopic observations that clearly show that Z CVn cannot be bound in such a binary. Therefore, the variations of pulsation period are likely intrinsic to the star. This finding represents a discovery/confirmation of a new type of cyclic period changes in RR Lyrae stars. By the analysis of our photometric data, we found that the Blazhko modulation with period of 22.931 d is strongly dominant in amplitude. The strength of the phase modulation varies and is currently almost undetectable. We also estimated photometric physical parameters of Z CVn and investigated their variations during the Blazhko cycle using the Inverse Baade-Wesselink method.
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