In her thesis [Commun. Algebra 23, No. 1, 219-243 (1995)], \textit{Maria Pia Solèr}, a student of the late H. Gross, proved that for every infinite dimensional hermitian space \((E, \langle\;\rangle)\) over a skew field \(K\) which is orthomodular, i.e. every subspace \(X\) of \(E\) satisfies \[ \text{if } X= (X^\perp )^\perp \quad \text{then} \quad E= X\oplus X^\perp, \tag{1} \] and which contains an orthonormal sequence \((e_n )_{n\in \mathbb{N}}\), necessarily \(K\) is \(\mathbb{R}\), \(\mathbb{C}\) or \(\mathbb{H}\) and \((E, \langle\;\rangle)\) is a Hilbert space over \(K\). In [\textit{H. A. Keller}, \textit{U. M. Künze} and \textit{M. P. Solèr}, `Orthomodular spaces' (to appear)] a simplification for the case of \(K\) being commutative is given. The aim of this paper is to present another simplification for the commutative case which carries over to the non-commutative case almost literally (see Section 5). The theorem we are going to prove first in the commutative case reads as follows: Theorem. Let \(K\) be a field, \({}^*: K\to K\) an involution on \(K\), \(E\) an infinite dimensional \(K\)-vector space, and \(\langle\;\rangle: E\times E\to K\) a hermitian form on \(E\). Then the only cases in which \((E,\langle\;\rangle)\) is orthomodular and contains an infinite orthonormal sequence \((e_n )_{n\in \mathbb{N}}\) occur if \((K,{}^*)= (\mathbb{R}, id)\) or \((\mathbb{C}, {}^-)\) and \((E,\langle\;\rangle)\) is a Hilbert space over \((K, {}^*)\). Although the proof given here is considerably shorter than the original one, it still uses the main ideas of M. P. Solèr.