We introduce a fully automated static analysis that takes a sequential Java bytecode program P as input and attempts to prove that there exists an infinite execution of P. The technique consists in compiling P into a constraint logic program P_CLP and in proving non-termination of P_CLP; when P consists of instructions that are exactly compiled into constraints, the non-termination of P_CLP entails that of P. Our approach can handle method calls; to the best of our knowledge, it is the first static approach for Java bytecode able to prove the existence of infinite recursions. We have implemented our technique inside the Julia analyser. We have compared the results of Julia on a set of 113 programs with those provided by AProVE and Invel, the only freely usable non-termination analysers comparable to ours that we are aware of. Only Julia could detect non-termination due to infinite recursion.