Aims. Following the first detection of hydrogen isocyanide (HNC) in Titan's atmosphere, we have devised a new neutral chemical scheme for hydrogen cyanide (HCN) and HNC in the upper atmosphere of Titan. Methods. Our updated chemical scheme contains 137 compounds (with C, H, O and N elements) and 788 reactions (including 91 photolysis processes). To improve the chemistry of HNC and HCN, a careful review of the literature has been performed to retrieve critical reaction rates and to evaluate their uncertainty factors. We have also estimated the reaction rates of 48 new reactions using simple capture theory. Results. Our photochemical model gives abundances of HNC and HCN in reasonable agreement with observations. An uncertainty propagation study shows large uncertainties for HNC and relatively moderate uncertainties for HCN. A global sensitivity analysis pinpoints some key reactions to study as a priority to improve the predictivity of the model. Conclusions. In particular, our knowledge of the isomerization of HNC via the reaction H + HNC → HCN + H and the chemistry of H 2 CN needs to be improved. This study of the neutral chemistry taking place in the upper atmosphere of Titan is a prerequisite for future ionospheric models since ion-neutral reactions may also contribute significantly to HNC and HCN production.