The orientations of the discontinuities in the solar wind, which correspond to southward (NS) and northward (SN) rotations of IMF, are analyzed. It is shown that different orientations take place and moderately inclined discontinuities prevail (in 60% of the cases considered). It is demonstrated in the analysis of successive NS and SN orientations that they are frequently not parallel to one another (the angle between the discontinuities exceeds 30° for 45% of the cases considered). This results in different estimates of duration of southward IMF influence on magnetosphere depending on spacecraft location in the solar wind. Using the data of four spacecraft, an event with a system of four successive discontinuities in the solar wind is considered in detail to illustrate these regularities. Different methods for the determination of the orientation of discontinuities are compared.