We analyze the standard model gauge group SU(3) × SU(2) × U(1) constructed in F-theory. The non-Abelian part SU(3) × SU(2) is described by a surface singularity of Kodaira type. Blow-up analysis shows that the non-Abelian part is distinguished from the naïve product of SU(3) and SU(2), but that it should be a rank three group along the chain of En groups, because it has non-generic gauge symmetry enhancement structure responsible for desirable matter curves. The Abelian part U(1) is constructed from a globally valid two-form with the desired gauge quantum numbers, using a similar method to the decomposition (factorization) method of the spectral cover. This technique makes use of an extra section in the elliptic fiber of the Calabi-Yau manifold, on which F-theory is compactified. Conventional gauge coupling unification of SU(5) is achieved, without requiring a threshold correction from the flux along the hypercharge direction.