  Given a sufficiently large and sufficiently dense bipartite graph $G=(A, B;
E),$ we present a novel method for decomposing the majority of the edges of $G$
into quasirandom graphs so that the vertex sets of these quasirandom graphs
partition the majority of $A.$ The method works for relatively small or sparse
graphs, and can be used to substitute the Regularity lemma of Szemer\'edi in
some graph embedding problems.
