Abstract: A boundary integral equation for describing a nonlinear force-free magnetic field with the finite energy content in the open space above the solar surface was proposed (Yan & Sakurai, 2000), which contains the boundary magnetic field and its normal gradient under the right integral sign. We present a new direct boundary integral equation in terms of the boundary magnetic field only. While calculating magnetic field values at space points by Yan’s equation, we must first calculate the normal gradient of the magnetic field at the boundary, and it must take much time to calculate the magnetic normal gradient; but while calculating magnetic field by the new direct equation, we need not calculate the magnetic normal gradient. Compared with Yan’s equation, to calculate the field using this new equation has the advantages of speediness and nicety.

Key words: solar magnetic fields, solar corona, solar active region