A 4-dimensional Walker metric on a semi Riemanian manifold $M$, for the canonical metric with $c=0$, have been investigated by M. Chaichi, E. Garc\'{\i}a--R\'{\i}o and Y. Matsushita. The paper generalizes these notions to the case of constant $c\ne 0$.
Specially the form of defining functions of this metric in locally conformally flat 4-dimensional Walker manifolds is found.