  The resistance of a metal in a magnetic field can be very illuminating about
its ground state. Some famous examples include the integer and fractional
quantum Hall effects\cite{Klitzing-QHE,Tsui-FQHE}, Shubnikov-de Haas
oscillations\cite{SdH}, and weak localization\cite{Lee-WL} \emph{et al}. In
non-interacting metals the resistance typically increases upon the application
of a magnetic field\cite{Pippard-MR}. In contrast, in some special
circumstances metals, with anisotropic Fermi surfaces\cite{Kikugawa-PdCoO2LMR}
or a so-called Weyl semimetal for instance\cite{Nielsen-ABJ,Son-ChirAnom}, may
have negative magnetoresistance. Here we show that semimetallic TaAs$_2$
possesses a gigantic negative magnetoresistance ($-$98\% in a field of 3 T at
low temperatures), with an unknown mechanism. Density functional calculations
illustrate that TaAs$_2$ is a new topological semimetal [$\mathbb{Z}_2$
invariant (0;111)] without a Dirac dispersion. This demonstrates that the
presence of negative magnetoresistance in non-magnetic semimetals cannot be
uniquely attributed to the Adler-Bell-Jackiw anomaly of bulk Dirac/Weyl
fermions. Our results also imply that the OsGe$_2$-type monoclinic dipnictides
are likely a material basis where unconventional topological semimetals may be
found.
