A matrix pencil \(\lambda Y-X\) of order \(m\) is called an eigenpencil of a matrix pencil \(\lambda B-A\) or order \(n>m\) if there exist \(n\times m\) matrices \(V\) and \(W\) of rank \(m\) such that \((\lambda B-A)V=W(\lambda Y-X)\). The authors show that, if an eigenpencil is known, it may be used to extend the Wielandt deflation for regular matrix pencils to a block context.