Let ${phi}$ be a map of a manifold M into another manifold N, L(N) the bundle of all linear frames over N, and ${phi}^{-1}$(L(N)) the bundle over M which is induced from ${phi}$ and L(N). Then, we construct a structure equation for the torsion form in ${phi}^{-1}$(L(N)) which is induced from a torsion form in L(N).