Search for neutrinoless ββ decay in 134Xe

New results have been obtained by investigating the neutrinoless ββ decay in 134Xe deep underground at the Gran Sasso National Laboratory of INFN by means of the ≃6.5 kg liquid xenon setup of the DAMA experiment. New limits on the half-lives of the β−β−0ν(0+→0+) and β−β−0ν(0+→2+) decay modes have been obtained. They are: T1/2>5.8×1022 yr (90% C.L.) and T1/2>2.6×1022 yr (90% C.L.), respectively. The T1/2 limit for β−β−0ν(0+→0+) process is about three orders of magnitude higher than the one previously available, while the T1/2 limit for β−β−0ν(0+→2+) has been set for the first time.