The NCO+C(2)H(2) reaction has been considered as a prototype for understanding the chemical reactivity of the isocyanate radical towards unsaturated hydrocarbons in fuel-rich combustion. It has also been proposed to provide an effective route for formation of oxazole-containing compounds in organic synthesis, and might have potential applications in interstellar processes. Unfortunately, this reaction has met mechanistic controversy both between experiments and between experiments and theoretical calculations. In this paper, detailed theoretical investigations at the Becke's three parameter Lee-Yang-Parr-B3LYP6-31G(d), B3LYP6-311++G(d,p), quadratic configuration interaction with single and double excitations QCISD6-31G(d), and Gaussian-3 levels are performed for the NCO+C(2)H(2) reaction, covering various entrance, isomerization, and decomposition channels. Also, the highly cost-expensive coupled-cluster theory including single and double excitations and perturbative inclusion of triple excitations CCSD(T)/aug-cc-pVTZ single-point energy calculation is performed for the geometries obtained at the Becke's three parameter Lee-Yang-Parr-B3LYP6-311++G(d,p) level. A previously ignored yet most favorable channel via a four-membered ring intermediate with allyl radical character is found. However, formation of P(3) H+HCCNCO and the five-membered ring channel predicted by previous experimental and theoretical studies is kinetically much less competitive. With the new channel, master equation rate constant calculations over a wide range of temperatures (298-1500 K) and pressures (10-560 Torr) show that the predicted total rate constants exhibit a positive-temperature dependence and no distinct pressure dependence effect. This is in qualitative agreement with available experimental results. Under the experimental conditions, the predicted values are about 50% lower than the latest experimental results. Also, the branching ratio variations of the fragments P(2) HCN+HCCO and P(5) OCCHCN+H as well as the intermediates L1 HCHCNCO, r4 cCHCHNC-O, and L5 NCHCHCO are discussed with respect to the temperature and pressure. Future experimental reinvestigations are strongly desired to test the newly predicted channel for the model NCO+C(2)H(2) reaction. Implications of the present results in various fields are discussed.