A special case of G-equivariant degree is defined, where G = ℤ₂, and the action is determined by an involution $T:{ℝ}^p\oplus {ℝ}^q\to {ℝ}^p\oplus {ℝ}^q$ given by T(u,v) = (u,-v). The presented construction is self-contained. It is also shown that two T-equivariant gradient maps $f,g:(ℝⁿ,S^{n-1})\to (ℝⁿ,ℝⁿ\setminus 0)$ are T-homotopic iff they are gradient T-homotopic. This is an equivariant generalization of the result due to Parusiński.