  A two-leg spin-1/2 ladder with diagonal interactions is investigated
numerically. We focus our attention on the possibility of columnar dimer phase,
which was recently predicted based on a reformulated bosonization theory. By
using density matrix renormalization group technique and exact diagonalization
method, we calculate columnar dimer order parameter, spin correlation on a
rung, string order parameters, and scaled excitation gaps. Carefully using
various finite-size scaling techniques, our results show no support for the
existence of columnar dimer phase in the spin ladder under consideration.
