A Potassium Titanyl Phosphate (KTP) crystal has been used in conjunction with a 10-ps pulsed laser to produce a frequency-doubled conically-refracted Gaussian beam. The ‘free’ and ‘forced’ beams that make up the scheme for nonlinear conical refraction were readily observable in non-phase-matched conditions. The dependency of the frequency-doubled beam patterns on the incident beam polarization, which until now has remained unexplored, was examined in detail. We have also revealed the existence of two orthogonally polarized ‘free’ rays for particular orientations of the incident beam polarization.