  V CVn is a semiregular variable star with a V-band amplitude of $\approx2$
mag. This star has an unusually high amplitude of polarimetric variability: up
to 6 per cent. It also exhibits a prominent inverse correlation between the
flux and the fraction of polarization and a substantial constancy of the angle
of polarization. To figure out the nature of these features, we observed the
object using the Differential Speckle Polarimetry at three bands centered on
550, 625 and 880 nm using the 2.5-m telescope of Sternberg Astronomical
Institute. The observations were conducted on 20 dates distributed over three
cycles of pulsation. We detected an asymmetric reflection nebula consisting of
three regions and surrounding the star at the typical distance of 35 mas. The
components of the nebula change their brightness with the same period as the
star, but with significant and different phase shifts. We discuss several
hypotheses that could explain this behavior.
