Spin vectors of 60 galaxies in the ''Ursa Major filament'' are obtaine
d from CCD images and spectroscopic determinations of the directions o
f rotation. These data are used to remove the fourfold degeneracy intr
oduced by the projected images of galaxies, making possible the comple
te reconstruction of the galaxy spin vectors. Several possible organiz
ations of spin vectors are investigated by means of statistical analys
es of the three-dimensional spin vector maps. The results indicate tha
t there exists no significant alignment of galaxy spin vectors with re
spect to the supergalactic plane, the supergalactic axis, or the cylin
drical axis of the filament itself. No tendency for linear alignment o
f spin vectors toward any specific direction was detected. We also obt
ain a statistically negative result for azimuthal, radial, and circula
r-helical orientation of spin vectors.