A direct numerical simulation of two-dimensional fuel jet flames developed in a co-flowing air stream was made considering rather complex finite chemistry in order to clarify the role of elementary reactions in flame structure and its unsteady behavior. The governing equations were discretized and numerically integrated using the finite volume method. The temperature dependence of thermodynamical properties was taken into account and the transport properties were calculated according to the simplified transport model proposed by Smooke [Reduced Kinetic Mechanisms and Asymptotic Approximations for Methane-Air Flames, (1991), p.1-28, Springer-Verlag]. Chemical reactions were described by Smooke's skeletal methane-air reaction mechanism. It was found that large-scale fluctuations were produced in the downstream of the jet flame where a decrease in temperature occurred at some instant, leading to local extinction. Upon comparison with the results of a counterflow laminar diffusion flame, it was also found that the hypothesis of the laminar flamelet model could be accepted even for the case of the unsteady jet flame with local extinction. Furthermore, better understanding of the extinction mechanism was obtained : In the turbulent region of the flame, fuel is converted by large vortices into the reaction zone at high supply rates, inducing CH3, CH3O, CH2O and HCO production. At some instant, the increase in mixing rates will result in a decrease in temperature, causing the consumption of available active radicals due to the activity of some exothermic reactions, and the slowdown of the reactions producing new OH, O and H radicals. The radical pool is no longer available for chain reactions to proceed, resulting in an extinction.