  We investigate Lie symmetries of Einstein's vacuum equations in N dimensions,
with a cosmological term. For this purpose, we first write down the second
prolongation of the symmetry generating vector fields, and compute its action
on Einstein's equations. Instead of setting to zero the coefficients of all
independent partial derivatives (which involves a very complicated substitution
of Einstein's equations), we set to zero the coefficients of derivatives that
do not appear in Einstein's equations. This considerably constrains the
coefficients of symmetry generating vector fields. Using the Lie algebra
property of generators of symmetries and the fact that general coordinate
transformations are symmetries of Einstein's equations, we are then able to
obtain all the Lie symmetries. The method we have used can likely be applied to
other types of equations.
