Let $n\in\mathbb N$, let $S_n$ denote the symmetric group of bijections $\{1,\dots,n\}\to\{1,\dots,n\}$, let $\lambda\vdash n$, and let $S^\lambda$ be the complex Specht $\mathbb C[S_n]$-module of shape $\lambda$. For $1\le k\le n$, define the Jucys-Murphy element $X_k\in\mathbb C[S_n]$ by $X_1:=0$ and, for $2\le k\le n$, by $X_k:=\sum_{1\le j<k}(j\ k)$, where $(j\ k)\in S_n$ is the transposition exchanging $j$ and $k$. For a standard Young tableau $T\in\operatorname{SYT}(\lambda)$ and an entry $k\in\{1,\dots,n\}$, let $\operatorname{row}_T(k)$ and $\operatorname{col}_T(k)$ denote respectively the row and column of the unique box containing $k$ in $T$, with rows and columns numbered starting at $1$. Define the content by $c_k(T):=\operatorname{col}_T(k)-\operatorname{row}_T(k)$. For $1\le i<n$, define the axial distance $r_i(T):=c_{i+1}(T)-c_i(T)$. For $1\le i<n$, let $s_i:=(i\ i+1)\in S_n$, and let $s_iT$ denote the filling obtained from $T$ by interchanging the entries $i$ and $i+1$. Then there exist a basis $(v_T)_{T\in\operatorname{SYT}(\lambda)}$ of $S^\lambda$ and a positive definite Hermitian form $(\cdot,\cdot):S^\lambda\times S^\lambda\to\mathbb C$ such that $(\sigma u,\sigma v)=(u,v)$ for all $\sigma\in S_n$ and all $u,v\in S^\lambda$, the basis $(v_T)$ is orthonormal, and $X_kv_T=c_k(T)v_T$ for every $T\in\operatorname{SYT}(\lambda)$ and every $1\le k\le n$. Moreover, for every $T\in\operatorname{SYT}(\lambda)$ and every $1\le i<n$, the following formulas hold. If $s_iT$ is not standard, then $s_iv_T=\frac{1}{r_i(T)}v_T$. If $s_iT$ is standard, then there exists a complex number $\gamma_i(T)$ with $|\gamma_i(T)|=1$ such that $s_iv_T=\frac{1}{r_i(T)}v_T+\gamma_i(T)\sqrt{1-r_i(T)^{-2}}\,v_{s_iT}$, where the square root denotes the positive real square root.