A study of the nucleus Ag106 has revealed the presence of two strongly coupled negative-parity rotational bands up to the 19- and 20- states, respectively, which cross each other at spin I∼14. The data suggest that near the crossover point the bands correspond to different shapes, which is different to the behavior expected from a pair of chiral bands. Inspection of the properties of these bands indicates a triaxial and a planar nature of rotation for the two structures. Possible causes for this may be understood in terms of a shape transformation resulting from the large degree of γ softness of Ag106. These data, along with the systematics of the odd-odd structures in the mass 100 region, suggest that γ softness has marked implications for the phenomenon of nuclear chirality.