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A new approach to the fabrication of a SrTiO/sub 3/ bicrystal substrates, based on floating zone growth of natural SrTiO/sub 3/ bicrystals with misorientation angles 24/spl deg/ and 37/spl deg/, has been developed. Thin film YBCO Josephson junctions and dc SQUIDs on SrTiO/sub 3/ bicrystal substrates were fabricated and studied at T=77 K. The critical current density j/sub c/ and I/sub c/R/sub n/ product for the junctions with misorientation angle /spl alpha/=24/spl deg/ were close to 2/spl times/10/sup 4/ A/cm/sup 2/ and 190-260 /spl mu/V, respectively, while for /spl alpha/=37/spl deg/ it was found that j/sub c//spl ap/2/spl times/10/sup 3/ A/cm/sup 2/ and I/sub c/R/sub n//spl ap/90-120 /spl mu/V. The dc SQUIDs were made with typical inductances 20-80 pH, critical currents of 20-150 /spl mu/A and resulting voltage modulation 10-40 /spl mu/V. Noise measurements performed at 77 K revealed low 1/f noise with cut-off frequency about 10 Hz.