It is mistakenly believed that in a curved space, parallel transfer of a vector along a closed contour leads to a change in its direction. It is also erroneous to say that when a vector moves along different trajectories at the end point, its directions turn out to be different. Evidence of the fallacy of these statements is provided. It is mistakenly believed that in a curved space, the parallel transfer of a vector along a closed contour leads to a change in its direction. It is also erroneous to say that when the vector moves along different trajectories at the end point, its directions turn out to be different. The proofs of the fallacy of these statements are given.