  We study the spin ladder model with interactions between spins on neighboring
rungs. The model Hamiltonian with the exact singlet ground state degenerated
with ferromagnetic state is obtained. The singlet ground state wave function
has a special recurrent form and depends on two parameters. Spin correlations
in the singlet ground state show double-spiral structure with period of spirals
equals to the system size. For special values of parameters they have
exponential decay. The spectrum of the model is gapless and there are
asymptotically degenerated excited states for special values of parameters in
the thermodynamic limit.
