  This paper develops a new fifth order accurate Hermite WENO (HWENO)
reconstruction method for hyperbolic conservation schemes in the framework of
the two-stage fourth order accurate temporal discretization in [{\em J. Li and
Z. Du, A two-stage fourth order time-accurate discretization {L}ax--{W}endroff
type flow solvers, {I}. {H}yperbolic conservation laws, SIAM, J. Sci. Comput.,
38 (2016), pp.~A3046--A3069}]. Instead of computing the first moment of the
solution additionally in the conventional HWENO or DG approach, we can directly
take the {\em interface values}, which are already available in the numerical
flux construction using the generalized Riemann problem (GRP) solver, to
approximate the first moment. The resulting scheme is fourth order temporal
accurate by only invoking the HWENO reconstruction twice so that it becomes
more compact. Numerical experiments show that such compactness makes
significant impact on the resolution of nonlinear waves.
