  A plane non-parallel flow in a square fluid domain exhibits an odd number of
vortices. A spectral structure is found to have a non-real solution of the
spectral problem linearized around the flow. With the use of this structure,
Hopf bifurcation or secondary time periodic flows branching of a basic square
eddy flow is found. In contrast to a square eddy flow involving an even number
of vortices in earlier analytical and experimental investigations, instability
of the flow leads to steady-state bifurcations.
