  Let $D\geq 3$ denote an integer. For any $x\in \mathbb F_2^D$ let $w(x)$
denote the Hamming weight of $x$. Let $X$ denote the subspace of $\mathbb
F_2^D$ consisting of all $x\in \mathbb F_2^D$ with even $w(x)$. The
$D$-dimensional halved cube $\frac{1}{2}H(D,2)$ is a finite simple connected
graph with vertex set $X$ and $x,y\in X$ are adjacent if and only if
$w(x-y)=2$. Fix a vertex $x\in X$. The Terwilliger algebra $\mathcal T=\mathcal
T(x)$ of $\frac{1}{2}H(D,2)$ with respect to $x$ is the subalgebra of ${\rm
Mat}_X(\mathbb C)$ generated by the adjacency matrix $A$ and the dual adjacency
matrix $A^*=A^*(x)$ where $A^*$ is a diagonal matrix with $$ A^*_{yy}=D-2w(x-y)
\qquad \hbox{for all $y\in X$}. $$ In this paper we decompose the standard
$\mathcal T$-module into a direct sum of irreducible $\mathcal T$-modules.
