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 effectscite{Klitzing-QHE,Tsui-FQHE}, Shubnikov-de Haas oscillationscite{SdH}, and weak localizationcite{Lee-WL} emph{et al}. In non-interacting metals the resistance typically increases upon the application of a magnetic fieldcite{Pippard-MR}. In contrast, in some special circumstances metals, with anisotropic Fermi surfacescite{Kikugawa-PdCoO2LMR} or a so-called Weyl semimetal for instancecite{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.
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