  Using a series expansion based on the flow-equation method we study the
ground state energy and the elementary triplet excitations of a generalized
model of crossed spin-1/2 chains starting from the limit of decoupled
quadrumers. The triplet dispersion is shown to be very sensitive to the
inter-quadrumer frustration, exhibiting a line of almost complete localization
as well as lines of quantum phase transitions limiting the stability of the
valence-bond solid phase. In the vicinity of the checkerboard-point a finite
window of exchange couplings is found with a non-zero spin-gap, consistent with
known results from exact diagonalization. The ground state energy is lower than
that of the bare quadrumer case for all exchange couplings investigated. In the
limiting situation of the fully frustrated checkerboard magnet our results
agree with earlier series expansion studies.
