Abstract: The space expansion for each component of the magnetic field without symmetric plane is derived in Cartesian coordianate system, which is in Taylor series of z. The coefficients of the expansions are expressed with the three components of the field and their partial derivatives with respect to x and y in a given plane z = z_0. The bicubic spline function fit of the discrete field distributions in the given plane is discussed, and the space expansions of the field represented with spline functions are further developed.