We present a new variational method for calculating complex resonance (Siegert) states in unimolecular dissociation reactions. The approach is based on the log-derivative version of the Kohn variational principle. The basic matrix equations can be formulated in terms of scattering-wave boundary conditions yielding the resonance states as homogeneous solutions for singular energies. Thus, the resonance positions and widths can be calculated directly without employing an artificial absorbing potential. This method is applied to the photodissociation of HCO and DCO and the results are compared to the resonance parameters obtained from absorption-type spectra.