  The current paper is dedicated to the problem of finding the number of
mutually non isomorphic bipartite graphs of the type $g=\langle R_g ,C_g ,E_g
\rangle$ at given $n=|R_g |$ and $m=|C_g |$, where $R_g$ and $C_g$ are the two
disjoint parts of the vertices of the graphs $g$, and $E_g$ is the set of
edges, $Eg \subseteq R_g \times C_g$. For this purpose, the concept of
canonical binary matrix is introduced. The different canonical matrices
unambiguously describe the different with exactness up to isomorphism bipartite
graphs. We have found a necessary and sufficient condition an arbitrary matrix
to be canonical. This condition could be the base for realizing recursive
algorithm for finding all $n \times m$ canonical binary matrices and
consequently for finding all with exactness up to isomorphism binary matrices
with cardinality of each part equal to $n$ and $m$.
