In this paper we propose a new apploximation of upwlnd streamlines in a framework of the Hermitian characteristic Galerkin ( HCG ) method for advection diffusion problems , The HCG method applies the Hermitian type elemen も which can improve accuracy of もhe characteristic Galerkin method . We present a new high order me 七hod using 七he Newmark scheme for the approxima 七 ion of upw 洫 d streamlines , which is often used for the dynamic structural analysis . We show the effectiveness of the present method by evaluating the computational accuracy ,