  Effect of four-spin cyclic exchange on magnetism is studied in the two-leg
S=1/2 ladder. We develop an exact spin-chirality duality transformation, under
which the system is self-dual when the four-spin exchange J_4 is half of the
two-spin exchange. Using the density-matrix renormalization-group method and
the duality relation, we find that the four-spin exchange makes the vector
chirality correlation dominant. A "chirality short-range
resonating-valence-bond" phase is identified for the first time at large J_4.
