It is proved that any harmonic map φ :Ω→Sp(N) from a simply connected domain ΩR2∪｛∞｝　 into the symplectic group Sp(N)U(2N) with finite uniton number can be factorized into a product of a finite number of symplectic unitons. Based on this factorization, it is proved that the minimal symplectic uniton number of φ is not larger than N, and the minimal uniton number of φ is not larger than 2N-1. The latter has been shown in literature in a quite different way.