A pair of stable noncanonical scalar vortices of the same charge is generated experimentally across the cross section of an optical beam using a computer-generated hologram with higher-order fractional screw dislocation. The noncanonical nature of the generated vortices is identified by the gradient of the phase around each vortex and also the crossing angle between the zero contours of the real and imaginary parts of the optical field. The anisotropy of the vortices is controlled by the fractional order of the computer-generated hologram. The behavior of the rate of change of phase around each individual vortex is found to be different from that of the earlier reports on noncanonical vortices. The observed experimental results are qualitatively explained based on the effect of nonlocalized phases of the generated vortices. The generated beams with a nested pair of noncanonical vortices can be of importance in accelerated rotation of the beams and in optical micromanipulation.