We report measurements of the radiative decay B→K*γ. The analysis is based on a data sample containing 85.0 × 10 6 B meson pairs collected by the Belle detector at the KEKB storage ring. We measure branching fractions of β(B 0→K* 0γ) = (4.01±0.21±0.17)× 10 -5 and β(B + →K* + γ) = (4.25±0.31±0.24)× 10 -5, where the first and second errors are statistical and systematic, respectively. The isospin asymmetry between B 0 and B + decay widths is measured to be Δ 0+ = + 0.012±0.044±0.026, assuming an equal production rate for B 0B̄ 0 and B +B - pairs from the γ(4S) resonance. We search for a partial rate asymmetry between CP conjugate modes, and find A CP(B→K*γ) = -0.015±0.0447plusmn;0.012.