The main objective of this talk is to introduce a high-order implicit time integration method and it's diagonalized variant for the solution of the time-dependent Navier-Stokes equations. The original method requires the inversion of block-tridiagonal system of equations which is a very time consuming task. A diagonalized version of the time-integration will be described and the computational efficiency and accuracy of the two time-integration methods will be compared. The implementation of the high-order right-hand-side in curvilinear coordinates, a new treatment of the cross-diffusion and the left-hand side treatment for cache-based computers will be described. Numerical examples from a DNS of turbulence in a channel will be used to demonstrate the current numerical approach.