The authors show that the rotation of the vector field for operators describing the traveling wave solutions \(u(x,t)=w(x-ct)\) of parabolic systems \(\partial u/\partial t=a\partial^ 2u/\partial x^ 2+F(u)\) can be constructed under an appropriate choice of spaces. Here a is a symmetric, positive-definite, square matrix of order n, \(u=(u_ 1,...,u_ n)\), \(F=(F_ 1,...,F_ n)\), \(x\in {\mathbb{R}}^ 1\) and \(t>0\).