We define $\bar x^i=x^i+v^i(x)\delta t$ as the $h$-curvature collineation of a Finsler space, supposing that the Lie derivative of Bervald's curvature tensor is equal to zero. Then we prove that every motion and every homothetic transformation admitted in a Finsler space are $H$-curvature collineations. Some special cases are also discussed.