Based on the inverse scattering method, the formulae of one higher‐order pole solitons and multiple higher‐order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. Their denominators are expressed as det(I+Ω∗Ω), where Ω is a matrix frequently constructed for solving the Riemann‐Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving I+Ω∗Ω is invertible. The first one shows matrix Ω is equivalent to a self‐adjoint Hankel matrix Δ, proving det(I+Ω∗Ω)=det(I+Δ†Δ)≥1. The second one considers the block‐matrix form of det(I+Ω∗Ω), proving |det(I+Ω∗Ω)|≥1. In addition, we prove that the dimension of Ω is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis.