  This paper deals with a new fifth-order weighted essentially non-oscillatory
(WENO) scheme improving the WENO-NS and WENO-P methods which are introduced in
Ha et al. J. Comput. Phys. (2013) and Kim et al., J. Sci. Comput. (2016)
respectively. These two schemes provide the fifth-order accuracy at the
critical points where the first derivatives vanish but the second derivatives
are non-zero. In this paper, we have presented a scheme by defining a new
global-smoothness indicator which shows an improved behavior over the solution
to the WENO-NS and WENO-P schemes and the proposed scheme attains optimal
approximation order, even at the critical points where the first and second
derivatives vanish but the third derivatives are non-zero.
