Explicit expression of Foldy-Wouthuysen transformation

The general, explicit and formally closed expression of arbitrary n-times Foldy-Wouthuysen transformations is clearly and strictly derived out. It is proved that if transformed Hamiltonian needs to be approximated to the order 1/m(K) or mv(2K) when to involve the orders of the operators, then to make N [(K + 1)/2]-times Foldy-Wouthuysen transformations is just enough ("[...]" means to take the part of integer). An example in non-relativistic quantum chromodynamics is given.