  The two-step time discretization proposed by Dahlquist, Liniger and
Nevanlinna is variable step $G$-stable. (In contrast, for increasing time
steps, the BDF2 method loses $A$-stability and suffers non-physical energy
growth in the approximate solution.) While unexplored, it is thus ideal for
time accurate approximation of the Navier-Stokes equations. This report
presents an analysis, for variable time-steps, of the method's stability and
convergence rates when applied to the NSE. It is proven that the method is
variable step, unconditionally, long time stable and second order accurate.
Variable step error estimates are also proven. The results are supported by
several numerical tests.
