  A new algorithm is presented to perform the full kinematic reconstruction of
top quark pair events produced at future electron-positron colliders in the
case of dilepton decays of the $W$ bosons to electrons or muons. The momentum
components of the undetected neutrino and anti-neutrino in the event are
reconstructed by employing several kinematic conditions comprising a non-linear
system of six equations. This system is solved numerically using two
independent methods and the selection of the best candidate real solution for
each event is determined by a likelihood discriminant. Results are presented
for several reconstructed kinematic properties of the $W^\pm$ bosons, top (and
anti-top) quarks using generator level information produced at leading order.
