Let \(j \geq 2\) be a natural number. For graphs \(G\) and \(H\), the size multipartite Ramsey number \(m_j(G, H)\) is the smallest natural number \(t\) such that any \(2\)-coloring by red and blue on the edges of \(K_{j \times t}\) necessarily forces a red \(G\) or a blue \(H\) as subgraph. Let \(P_n\) be a path on \(n\) vertices. In this note, we determine the exact value of the size multipartite Ramsey number \(m_j(P_4, P_n)\) for \(n \geq 2\).