Let $P$ be a finite graded poset with rank function $\rho:P\to\mathbb{N}\cup\{0\}$, and let $\lambda$ be an EL-labeling of the cover relations of $P$ by elements of a totally ordered label set $\Lambda$, meaning that on every bounded interval the lexicographically first saturated maximal chain is the unique chain whose label word is weakly increasing. Let $x,y\in P$ satisfy $x\le y$, and equip the interval $[x,y]=\{z\in P:x\le z\le y\}$ with the inherited EL-labeling, namely the restriction of $\lambda$ to cover relations contained in $[x,y]$. Define $r=\rho(y)-\rho(x)$. Let $\mu_P$ denote the Möbius function of the finite poset $P$. Define $f:\{(u,v)\in P\times P:u\le v\}\to\mathbb{N}\cup\{0\}$ by letting $f(u,v)$ be the number of saturated maximal chains $u=u_0\lessdot u_1\lessdot \cdots \lessdot u_s=v$ in $[u,v]$ whose label word $\lambda(u_0,u_1),\lambda(u_1,u_2),\dots,\lambda(u_{s-1},u_s)$ is strictly decreasing in the order on $\Lambda$. For $u=v$, the interval $[u,u]$ is assigned one empty falling maximal chain, so $f(u,u)=1$. Then $\mu_P(x,y)=(-1)^r f(x,y)$.