The authors examine the magnetic configuration of a one-turn helical magnetic field in the presence of an axial current. Particular attention is paid to the properties of the rotational transform of the magnetic field lines and to the minimum of the mean magnetic field. A relationship is found between negative V"(ø) and shear, on the one hand, and the structural features of the configuration, on the other.It is shown at what parameter values the configuration in question possesses closed magnetic surfaces surrounding the helical axis, an angle of rotational transform, shear and a minimum of the mean magnetic field.