The helical instability of an arc column with electrical conductivity of the distribution of the linear heat flux potential (a new "temperature") is discussed in axial magnetic field. The magnetohy-drodynamic equations serve as the starting point of the theory. In an electrostatic approximation and a linear time dependent perturbation theory, the perturbation equations for the arc column movement are deduced. Solutions of these equations are obtained analytically, from which the stability limit of the cylindrical arc and the growth rate of the helical instability are given. In comparison the results with those of uniform current distribution, it is found that the stable area is enlarged.