Summary: Let \(R\) be a commutative local ring of characteristic 2, \(\text{Rad\,}R=tR\), \(t\in R\), \(t^2=0\), \(t\neq 0\), residue class field of ring \(R\) contains only one root of unity of degree \(p\). All matrix \(R\)-representations of 2-nd degree of dihedral group of order \(2p\) (\(p\) is an odd prime) are described up to equivalence.