Let \((E,\langle \cdot, \cdot\rangle)\) be a hermitean space over a skew field \(K\) \((\text{char } K\neq 2)\). \(E\) is said to be orthomodular if the following is satisfied: \(E= X\oplus X^\perp\), whenever \(X\) is a subspace of \(E\) with \(X= (X^\perp )^\perp\) (here we use the notation \(X^\perp= \{y\in E\mid \langle x, y\rangle =0\}\)). It has been proved by H. A. Keller in 1979 that there is an orthomodular space which is not isomorphic to a classical Hilbert space over reals, complexes, or quaternions. On the other side, the main result of the paper under review says that every infinite dimensional orthomodular space possessing an infinite orthonormal system is either real, complex, or quaternionic Hilbert space. Using the coordinatization theorem the author gets the lattice-theoretic form of this result: Every Hilbert lattice (i.e. irreducible, complete, atomistic, orthomodular, and \(M\)- symmetric lattice) is a classical Hilbert lattice (i.e. the lattice of all orthogonally closed subspaces in a standard Hilbert space).