The stability of the neutral current sheet is analyzed in the frame of Hall dynamics. The problem is treated analytically and results are verified by numerical processing. A new version of tearing instability is found and described. It scales more favorably with the Lundquist number and has smaller wavelengths. Combined Hall magnetohydrodynamic analysis shows that Hall effects dominate the diffusion layer and growth rate of the instability in a relatively large range of sheet widths. The effect of finite beta on instability is described.