  An edge cut $C$ of a graph $G$ is {\it tight} if $|C \cap M|=1$ for every
perfect matching $M$ of $G$.~Barrier cuts and 2-separation cuts are called {\it
ELP-cuts}, which are two important types of tight cuts in matching covered
graphs.~Edmonds, Lov\'asz and Pulleyblank proved that if a matching covered
graph has a nontrivial tight cut, then it also has a nontrivial
ELP-cut.~Carvalho, Lucchesi, and Murty made a stronger conjecture: given any
nontrivial tight cut $C$ in a matching covered graph $G$, there exists a
nontrivial ELP-cut $D$ in $G$ which does not cross $C$.~We confirm the
conjecture in this paper.
