It's proved that the nonzero linear combinations of the coordinates (NLCC for short) of a bijective monomial in a finite field of characteristic two are linearly equivalent

and the number of equivalent transformations is equal to the number of nonzero elements in the finite field.It's prove that the NLCCs of S-boxes of AES are linear equivalent

and the group formed by the zero transformation and all transformations constructed in this paper for equivalence of a given NLCC to NLCCs under the pointwise addition of transformations is isomorphic to additive group of the finite field.The equivalent transformations of the least significant coordinate to 8 coordinates are given

which is a base of this group.It's proved also that the sum of equivalent transformations of coordinates constructed by Fuller J and Millan W is not an equivalent transformation of two NLCCs of S-boxes of AES.