We report an astronomical detection of HC$_4$NC for the first time in the interstellar medium with the Green Bank Telescope toward the TMC-1 molecular cloud with a minimum significance of $10.5 sigma$. The total column density and excitation temperature of HC$_4$NC are determined to be $3.29^{+8.60}_{-1.20}times 10^{11}$ cm$^{-2}$ and $6.7^{+0.3}_{-0.3}$ K, respectively, using the MCMC analysis. In addition to HC$_4$NC, HCCNC is distinctly detected whereas no clear detection of HC$_6$NC is made. We propose that the dissociative recombination of the protonated cyanopolyyne, HC$_5$NH$^+$, and the protonated isocyanopolyyne, HC$_4$NCH$^+$, are the main formation mechanisms for HC$_4$NC while its destruction is dominated by reactions with simple ions and atomic carbon. With the proposed chemical networks, the observed abundances of HC$_4$NC and HCCNC are reproduced satisfactorily.
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