We present a nonlocal kinetic-energy functional which includes an anis
otropic average of the density through a symmetrization procedure. Thi
s functional allows a better description of the nonlocal effects of th
e electron system. The main consequence of the symmetrization is the a
ppearance of a clear shell structure in the atomic density profiles, o
btained after the minimization of the total energy. Although previous
results with some of the nonlocal kinetic functionals have given incip
ient structures for heavy atoms, only our functional shows a clear she
ll structure for most of the atoms. The atomic total energies have a g
ood agreement with the exact calculations. Discussion of the chemical
potential and the first ionization potential in atoms is included. The
functional is also extended to spin-polarized systems.