The author constructs by means of spherical functions \(P\) with respect to a symmetric matrix \(A\) Hilbert modular forms \(f\) of half-integral weight for principal congruence subgroups of level \(2N\) of the Hilbert modular group of a totally real number field of degree \(r\) and ring of integers \({\mathcal O}\). Such a spherical function is nothing but a homogeneous polynomial satisfying \(\text{tr (hess P.A}^{-1}) = 0\) which generalizes the usual definition \(\Delta P = 0\). The sought function \(f\) is given by \[ f(z) : = \sum_{u \in {\mathcal O}/(N)} \varphi (u)\Theta (z,u,A,N) \] where \(\varphi\) is a primitive character with conductor \(N\), \(A\) a diagonal matrix with integer entries and \(\Theta\) a theta-function with coefficients \(P(v^{(1)}, \ldots, v^{(r)})\), \(v \equiv u(N)\). Reviewer's note: The formulation of Lemma 5 is misleading.