We investigate the low-energy properties of the orthogonal-dimer spin chain
characterized by a frustrated dimer-plaquette structure. When the competin
g antiferromagnetic couplings are varied, the first-order quantum phase tra
nsition occurs between the dimer and the plaquette phases, which is accompa
nied by nontrivial features due to frustration. besides the discontinuity i
n the lowest excitation gap at the transition point, a sharp level crossing
occurs for the spectrum in the plaquette phase. We further reveal that the
plateau in the magnetization curve at 1/4 of the full moment dramatically
changes its character in the vicinity of the critical point. It is argued t
hat the first-order phase transition in this system captures some essential
properties found in the two-dimensional orthogonal-dimer model proposed fo
r SrCu2(BO3)(2).