  Within the linear flavor-wave theory, we show that, caused by quantum
order-by-disorder mechanism, the spin-1 bilinear-biquadratic Heisenberg model
defined on a honeycomb lattice can spontaneously develop a columnar dimer order
with a non-bipartite structure. The low-lying excitations above this novel
ground state form several flat bands separated by nonzero energy gaps. Our
results suggest that the quantum phase transition separating this dimerized
phase with the nearby N\'{e}el-order one may be of first order.
