A new high-spin isomer in the neutron-rich nucleus128Cd was populated in the projectile fission of a238U beam at the Radioactive Isotope Beam Factory at RIKEN. A half-life of T1/2=6.3(8) ms was measured for the new state which was tentatively assigned a spin/parity of (15−). The experimental results are compared to shell model calculations performed using state-of-the-art realistic effective interactions and to the neighbouring nucleus129Cd. In the present experiment no evidence was found for the decay of a 18+E6 spin-trap isomer, based on the complete alignment of the two-neutron and two-proton holes in the 0h11/2and the 0g9/2orbit, respectively, which is predicted to exist by the shell model.