  String theory in 4 dimensions has the unique feature that a topological term,
the oriented self-intersection number, can be added to the usual action. It has
been suggested that the corresponding theory of random surfaces wold be free
from the problem encountered in the scaling of the string tension.
Unfortunately, in the usual dynamical triangulation it is not clear how to
write such a term. We show that for random surfaces on a hypercubic lattice
however, the analogue of the oriented self-intersection number $I[\s]$ can be
defined and computed in a straightforward way. Furthermore, $I[\s]$ has a
genuine topological meaning in the sense that it is invariant under the
discrete analogue of continuous deformations. The resulting random surface
model is no longer free and may lead to a non trivial continuum limit.
