Let X be a separable Banach space, \(X^*\) be its dual and B(X) be its Borel field, where a probability measure \(\mu\) is given. The main results are the following: Theorem 1. Let \(\mu\) be ergodic w.r.t. Q, the set of all quasi-invariant directions of \(\mu\), and symmetric and \(X^*\subset L^ 2(X,\mu)\), then we can find a sequence \((a_ n)\) such that \((a_ n)\subset Q\) and, \[ [F,G]=\int F(x)G(x)d\mu =\sum_{n}F(a_ n)G(a_ n),\text{ for every } F,G\in X^*. \] The sequence \((a_ n)\) is called an orthogonal system of \(\mu\). Assume that \((a_ n)\) is an orthogonal system of \(\mu\). We say the measure \(\mu\) is normal if, for every n, the Radon-Nikodym derivate \(d\mu_{ta_ n}/d\mu (x)\), \(t\in [0,+\infty)\), \(x\in X\), is continuous on \([0,+\infty)\times X.\) Corollary. Every Gaussian measure on X is normal. Theorem 2. If \(\mu\) is a normal measure on X, which satisfies the conditions mentioned in Theorem 1, we define a symmetric form \(D_ 0\) which is defined densely on \(L^ 2(X,\mu)\), such that \[ D_ 0(u,v)=\int \sum_{i,j}[f_ i,g_ j]\partial \phi /\partial y_ i(f_ 1,f_ 2,...,f_ n)\partial \psi /\partial z_ j(g_ 1,g_ 2,...,g_ n)d\mu \] where, \(\phi \in C_ b(R^ n)\), \(\psi \in C_ b(R^ n)\); \(f_ i,g_ j\in X^*\), \(1\leq i\leq n\), \(1\leq j\leq n\), \(u(x)=\phi (f_ 1,f_ 2,...,f_ n)\), \(v(x)=\psi (g_ 1,g_ 2,...,g_ n)\), \(x\in X\). Then the form \(D_ 0\) is closable and its smallest extension D is a Dirichlet form. We understand the self-adjoint operator A, corresponding to this Dirichlet form D, as an analogy of the Laplace operator and call it the Laplace-Beltrami operator of the measure \(\mu\). It is well known that the Ornstein-Uhlenbeck operator is just the Laplace-Beltrami operator of some Gaussian measure on X.