  We discuss the distribution of radial velocities of galaxies belonging to the
Local Group. Two independent samples of galaxies as well as several methods of
reduction from the heliocentric to the galactocentric radial velocities are
explored. We applied the power spectrum analysis using the Hann function as a
weighting method, together with the jackknife error estimation. We performed a
detailed analysis of this approach. The distribution of galaxy redshifts seems
to be non-random. An excess of galaxies with radial velocities of $\sim 24 {km}
\cdot {s}^{-1}$ and $\sim 36 {km} \cdot {s}^{-1}$ is detected, but the effect
is statistically weak. Only one peak for radial velocities of $\sim 24 {km}
\cdot {s}^{-1}$ seems to be confirmed at the confidence level of 95%.
