A hybrid numerical boundary condition (HNBC) with the same accuracy as surface integral methods, applicable to an absorbing boundary with an arbitrary shape, is proposed. The HNBC is a global boundary condition resulting in a dense submatrix due to the coupling of all boundary nodes. In many cases, the HNBC can be approximated by another set of boundary conditions where only a few boundary nodes are coupled together to preserve the sparsity of the resulting matrix equation. One special approximation will result in the measured equation of invariance (MEI) method. Another approximation will result in a nonlocal numerical boundary condition (NNBC), of which the MEI method is a subset. For the NNBC, the sparsity of the resulting finite element matrix is preserved, although the boundary condition is nonlocal. Numerical results for a class of 2-D problems are presented to illustrate the accuracy of the original global hybrid numerical boundary condition and the nonlocal numerical boundary condition.