A method of manufacturing a sheet of copper-based alloy consisting of Ni: 0.01-4.0 wt.%, Sn: 0.01-10 wt.% and P: 0.01-0.20 wt.% and optionally containing at least one of the following: 20 ppm or less of O, 0.01 to 1.0 wt.% Si, 0.03-3.0 wt.% of Zn, 0.01-3.0 wt.% of at least one element selected from the group consisting of Fe, Co, Mg, Ti, Cr, Zr and Al, and 2 wt.% or less of at least one element selected from the group consisting of Ag, Au, Bi, In, Mn, La, Pb, Pd, Sb, Se, Te and Y, with the remainder being Cu and unavoidable impurities, where the x-ray diffraction intensity ratio of the surface S ND is such that 0.05 ≤ S ND ≤ 0.15, provided that S ND =I ÷ [I + I + I], where I is the x-ray diffraction intensity of the plane, I is the x-ray diffraction intensity of the plane, I is the x-ray diffraction intensity of the plane, and I is the x-ray diffraction intensity of the plane, the method comprising the steps of: taking an ingot of a copper-based alloy having the indicated elemental composition, performing at least one of homogenization annealing or hot rolling at 750°C to 900°C for 30 minutes to 2 hours; performing a combination process of cold rolling followed by intermediate annealing at 400°C to 700°C for 0,5 minutes to 10 hours at least one time, performing an intermediate cold rolling, which is a rolling process before a final cold rolling process, at a cold rolling reduction rate of 50 to 90 % to achieve 0.05 ≤ S ND ≤ 0.15 immediately followed by a finish annealing at 400°C to 700°C for 0,5 minutes to 10 hours to achieve a grain size of 20 microns or less, and then performing final cold rolling at a percent reduction Z that satisfies the following formula: 0.8 × 100 − 10 X − Y < Z < 100 − 10 ⁢ X − Y where Z is the percent cold reduction (%), X is the Sn content (wt.%) among the various elements, and Y is the total content (wt.%) of all elements other than Sn and Cu, followed by low-temperature annealing performed at 250°C to 350°C for 30 minutes to 2 hours. 20 ppm or less of O, 0.01 to 1.0 wt.% Si, 0.03-3.0 wt.% of Zn, 0.01-3.0 wt.% of at least one element selected from the group consisting of Fe, Co, Mg, Ti, Cr, Zr and Al, and 2 wt.% or less of at least one element selected from the group consisting of Ag, Au, Bi, In, Mn, La, Pb, Pd, Sb, Se, Te and Y, with the remainder being Cu and unavoidable impurities, where the x-ray diffraction intensity ratio of the surface S ND is such that 0.05 ≤ S ND ≤ 0.15, provided that S ND =I ÷ [I + I + I], where I is the x-ray diffraction intensity of the plane, I is the x-ray diffraction intensity of the plane, I is the x-ray diffraction intensity of the plane, and I is the x-ray diffraction intensity of the plane, the method comprising the steps of: taking an ingot of a copper-based alloy having the indicated elemental composition, performing at least one of homogenization annealing or hot rolling at 750°C to 900°C for 30 minutes to 2 hours; performing a combination process of cold rolling followed by intermediate annealing at 400°C to 700°C for 0,5 minutes to 10 hours at least one time, performing an intermediate cold rolling, which is a rolling process before a final cold rolling process, at a cold rolling reduction rate of 50 to 90 % to achieve 0.05 ≤ S ND ≤ 0.15 immediately followed by a finish annealing at 400°C to 700°C for 0,5 minutes to 10 hours to achieve a grain size of 20 microns or less, and then performing final cold rolling at a percent reduction Z that satisfies the following formula: 0.8 × 100 − 10 X − Y < Z < 100 − 10 ⁢ X − Y where Z is the percent cold reduction (%), X is the Sn content (wt.%) among the various elements, and Y is the total content (wt.%) of all elements other than Sn and Cu, followed by low-temperature annealing performed at 250°C to 350°C for 30 minutes to 2 hours. taking an ingot of a copper-based alloy having the indicated elemental composition, performing at least one of homogenization annealing or hot rolling at 750°C to 900°C for 30 minutes to 2 hours; performing a combination process of cold rolling followed by intermediate annealing at 400°C to 700°C for 0,5 minutes to 10 hours at least one time, performing an intermediate cold rolling, which is a rolling process before a final cold rolling process, at a cold rolling reduction rate of 50 to 90 % to achieve 0.05 ≤ S ND ≤ 0.15 immediately followed by a finish annealing at 400°C to 700°C for 0,5 minutes to 10 hours to achieve a grain size of 20 microns or less, and then performing final cold rolling at a percent reduction Z that satisfies the following formula: 0.8 × 100 − 10 X − Y < Z < 100 − 10 ⁢ X − Y where Z is the percent cold reduction (%), X is the Sn content (wt.%) among the various elements, and Y is the total content (wt.%) of all elements other than Sn and Cu, followed by low-temperature annealing performed at 250°C to 350°C for 30 minutes to 2 hours.