Linear force-free fields are often used as approximate models for magnetic
fields in the solar corona, calculated on the basis of boundary values meas
ured in the low atmosphere. The problem that is set up and solved does not
have a unique solution, however, and various particular solutions-motivated
in large part by mathematical convenience-appear in the literature. A meth
od is presented for calculating the linear force-free held that is consiste
nt with the observed component of the magnetic field normal to the solar su
rface and has a minimum difference between the components tangent to the su
rface and the observed tangential field. The method is tested by applicatio
n to a known tangent to the surface and the nonlinear solution.