A new conservation theorem is studied, the conserved quantity is only constructe d in terms of the infinitesimal generators τ(t,q,q·) and ξs( t,q,q· ) of Lie symmetry of the dynamical equations. Three special cases are discussed, where the Hojman conserved quantity can be deduced as a corollary of this gener al conservation theorem at τ(t,q,q·)=0, and the Lutzky conserved quantity can be derived by using this general conservation theorem at τ=τ(t,q) and ξs=ξs(t,q).Moreover, a condition is presented to exc lude trivial conse rved quantities. Finally, two examples to illustrate the application of the resu lts are given.
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