Let u1. . . , un and v1, . . . , vn be bases of a vector space (the interesting case, when the underlying field is finite). Then there exist vectors w1, . . . , wn-1, such that every n consecutive vectors in the sequence u1, . . . , un, W1, . . . , Wn-l, v1, . . . , vn from a basis. Similar statements hold in structures other then vector spaces. The case of a free Boolean algebra is shown equivalent to an open problem in switching network theory.