Given a binary relation R of basis E, we define its dual R*by R* (x, y) = R(y, x). A relation R is self-dual if it is isomorphic to R*. A binary relation R' is hemimorphic to R, if it is isomorphic to R or to R*. A binary relation R is d-half-reconstructible if it is determined by its restrictions of cardinality d, up to hemimorphism. In this paper we characterize the finite binary relations d-half-reconstructibile for every d <FONT FACE=Symbol>Îí</FONT>7, 8, 9, 10, 11<FONT FACE=Symbol>ý</FONT>.