A new notion of parity is used to construct a simple strong invariant of free knots taking values in some group. The interval of the set of positive integers is considered containing all integers from 1 to a given number 2n and a chord diagram with a base point is defined as a partition of the set. For any positive integer, the equivalence of two chord diagram with base points implies the coincidence of the elements of the group corresponding to the words. The elements of the group are in one-to-one correspondence with the integer points in Euclidean space with last coordinate 0 or 1. Any chord diagram containing a completely adjoint chords has the property that the number of odd chords are even. The removal of odd chords preserves the triple of completely adjoint chords and if the triple again contains no odd chords, the chords are denoted by a group.