Lifetimes of states in the lowest lying positive parity band in 106Cd have been measured using the Doppler shift attenuation method. The deduced B(E2) transition rates show a marked decrease with increasing spin. Cranking and semiclassical model calculations suggest that the structure has the character of a shears-type band resulting from the coupling of g(9/2) proton holes to aligned pairs of h(11/2) and g(7/2) neutron particles. This is the first clear evidence for the phenomenon of "antimagnetic" rotation in nuclei.