We present an improved QCD light-cone sum rule (LCSR) calculation of the B -> K and Bs -> K form factors, by including SU(3)-symmetry breaking corrections. We use recently updated K-meson distribution amplitudes which incorporate the complete SU(3)-breaking structure. By applying the method of the direct integration in the complex plane, which is presented in a detail, the analytical extraction of the imaginary parts of LCSR hard-scattering amplitudes becomes unnecessary and therefore the complexity of the calculation is greatly reduced. The values obtained for the relevant B_{(s)} -> K form factors are as follows: f^+_{BK}(0)= 0.36^{+0.05}_{-0.04}, f^+_{B_sK}(0)= 0.30^{+0.04}_{-0.03} and f^T_{BK}(0)= 0.38pm 0.05, f^T_{B_sK}(0)= 0.30pm 0.05. By comparing with the B -> pi form factors extracted recently by the same method, we find the following SU(3) violation among the B -> light form factors: f^+_{BK}(0)/f^+_{Bpi}(0) = 1.38^{+0.11}_{-0.10}, f^+_{B_sK}(0)/f^+_{Bpi}(0) = 1.15^{+0.17}_{-0.09}, f^T_{BK}(0)/f^T_{Bpi}(0) = 1.49^{+0.18}_{-0.06} and f^T_{B_sK}(0)/f^T_{Bpi}(0) = 1.17^{+0.15}_{-0.11}.
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