A MHD, symmetrical, nonpotential waves in nonuniform, cylindrical nonisothermal plasma waveguide placed in a finite external magnetic field H,, directed along the axis of the waveguide are considered. The thermal velocity of the electrons = (kT,/m,)1/2 (k -Boltzman's constant, Td -temperature, ma -mass of the electron) is not neglected. As a consequence we obtain one more solution in the plasma region and respectively an equation of third power on ~2 -the transverse wave number. As far as we know only equations of second power on xp describing non-potential waxes are investigated. The dispersion equations are written solving the boundaryvalue problem. Our results coincide with well known ones when the electron thermal velocity tends to zero.