  In this work, we introduce a new space-time variational formulation of the
second-order wave equation, where integration by parts is also applied with
respect to the time variable, and a modified Hilbert transformation is used.
For this resulting variational setting, ansatz and test spaces are equal. Thus,
conforming finite element discretizations lead to Galerkin--Bubnov schemes. We
consider a conforming tensor-product approach with piecewise polynomial,
continuous basis functions, which results in an unconditionally stable method,
i.e., no CFL condition is required. We give numerical examples for a one- and a
two-dimensional spatial domain, where the unconditional stability and optimal
convergence rates in space-time norms are illustrated.
