  In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of
compact Hausdorff spaces and continuous maps. The composition of the morphisms
of the dual category obtained by him differs from the set-theoretic one. Here
we obtain a new category dual to the category {\bf HLC} of locally compact
Hausdorff spaces and continuous maps for which the composition of the morphisms
is a natural one but the morphisms are multi-valued maps.
