Uniqueness of decomposition for positive-definite integral bilinear forms?

Question

Let $\Lambda$ be a lattice, that is a free finitely generated abelian group with a symmetric bilinear form.

In general, decomposition of lattices into indecomposable orthogonal sublattices is not unique. For example, if $U$ is a hyperbolic plane ($e_1^2 = e_2^2 = 0$, $e_1 \cdot e_2 = 1$), then $U \oplus \langle -1 \rangle \simeq \langle 1, -1, -1 \rangle$, however $U \not\simeq \langle 1, -1 \rangle$.

Is the orthogonal decomposition into indecomposables unique if we assume $\Lambda$ to be positive-definite?

Thanks!