A Direct Construction Method for Conservation Laws of Partial Differential Equations Stephen C Anco and George W Bluman*, Department of Mathematics, University of British Columbia, Vancouver BC Canada V6T 1Z2 We present a method to obtain all local conservation laws for any given system of partial differential equations. This method does not depend on the system having a Lagrangian formulation, in contrast to Noether's theorem which only applies to Lagrangian (i.e., self-adjoint) systems. Examples will be given. A preliminary version of this work recently appeared in Phys. Rev. Lett.