The Gröbner walk method is a conversion procedure proposed by Collart, Kalkbrener, and Mall (1997) with the aim of converting a given Gröbner basis, respect to a fixed monomial order, of a polynomial ideal I of the commutative polynomial ring K[x_1, ..., x_n] to a Gröbner basis of I with respect to another monomial order. Since some approaches have been realized to Gröbner walk method in the noncommutative setting for specific families of algebras, it is important to us to investigate the possibility of this procedure in the setting of Gröbner bases of another families of noncommutative algebras.