  We calculate the boundary correlation function of fixed-to-free boundary
condition changing operators in the square-lattice Ising model. The correlation
function is expressed in four different ways using $2\times2$ block Toeplitz
determinants. We show that these can be transformed into a scalar Toeplitz
determinant when the size of the matrix is even. To know the asymptotic
behavior of the correlation function at large distance we calculate the
asymptotic behavior of this scalar Toeplitz determinant using the Szeg\"o's
theorem and the Fisher-Hartwig theorem. At the critical temperature we confirm
the power-law behavior of the correlation function predicted by conformal field
theory.
