The stability of the magnetic field in the solar corona is important for understanding the causes of solar eruptions.Although various scenarios have been suggested to date, the tether-cutting reconnection scenario proposed byMoore et al. is one of the widely accepted models to explain the onset process of solar eruptions. Although thetether-cutting reconnection scenario proposes that the sigmoidal field formed by internal reconnection is themagnetic field in the pre-eruptive state, the stability of the sigmoidal field has not yet been investigatedquantitatively. In this paper, in order to elucidate the stability problem of the pre-eruptive state, we developed asimple numerical analysis in which the sigmoidal field is modeled by a double arc electric current loop and itsstability is analyzed. As a result, we found that the double arc loop is more easily destabilized than theaxisymmetric torus, and it becomes unstable even if the external field does not decay with altitude, which is incontrast to the axisymmetric torus instability. This suggests that tether-cutting reconnection may well work as theonset mechanism of solar eruptions, and if so, the critical condition for eruption under a certain geometry may bedetermined by a new type of instability rather than by the torus instability. Based on them, we propose a new typeof instability called double arc instability (DAI). We discuss the critical conditions for DAI and derive a newparameter κ, defined as the product of the magnetic twist and the normalized flux of the tether-cuttingreconnection.