  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.
