Let m $m$ and r $r$ be positive integers with r≥3 $r\ge 3$, let G $G$ be an r $r$‐regular cyclically ((m−1)r+1) $((m-1)r+1)$‐edge‐connected bipartite graph and let M $M$ be a matching of size m $m$ in G $G$. Plummer showed that whenever r≥m+1 $r\ge m+1$, there is a perfect matching of G $G$ containing M $M$. When r=3 $r=3$, Aldred and Jackson, extended this result to the case when m+1≥r=3 $m+1\ge r=3$ by showing there is a perfect matching in G $G$ containing M $M$ whenever the edges in M $M$ are pairwise at least distance f(m) $f(m)$ apart where f(m)=1,m=23,3≤m≤44,5≤m≤85,m≥9. $f(m)=\left\{\begin{array}{ll}1, & m=2\\ 3, & 3\le m\le 4\\ 4, & 5\le m\le 8\\ 5, & m\ge 9.\end{array}\right.$ In this paper, we relax the condition that r=3 $r=3$ and the distance restriction introduced by Aldred and Jackson to show that, for m≥r≥3 $m\ge r\ge 3$ and G $G$ an r $r$‐regular cyclically ((m−1)r+1) $((m-1)r+1)$‐edge‐connected bipartite graph, for each matching M $M$ in G $G$ with ∣M∣=m $| M| =m$ and such that each pair of edges in M $M$ is distance at least 3 apart, there is a perfect matching in G $G$ containing M $M$. [ABSTRACT FROM AUTHOR]