A search for instability of nucleons bound in Xe-136 nuclei is reported with 223 kg.yr exposure of Xe-136 in the EXO-200 experiment. Lifetime limits of 3.3 x 10(23) and 1.9 x 10(23) yr are established for nucleon decay to Sb-133 and Te-133, respectively. These are the most stringent to date, exceeding the prior decay limits by a factor of 9 and 7, respectively.