Let $M$ be a continuous local martingale with $M_0 = 0$. Then there exists a unique (up to indistinguishability) continuous adapted increasing process $(\langle M \rangle_t)_{t \ge 0}$ such that $\langle M \rangle_0 = 0$ and $M^2_t - \langle M \rangle_t$ is a continuous local martingale. Moreover, $\langle M \rangle$ is the u.c.p. limit of the Riemann-sum approximants \begin{align*} \langle M \rangle^{(n)}_t = \sum_{i=1}^{\lfloor 2^n t \rfloor} (M_{i \cdot 2^{-n}} - M_{(i-1) \cdot 2^{-n}})^2. \end{align*}