On complete interpolation spline finding via $B$-splines

We discuss a problem of interpolation by a complete spline of $2n-1$ degree given in $B$-spline representation. It is shown that the first $n$ and the last $n$ coefficients of $B$-spline decomposition are under explicit formulas and other coefficients can be found as a solution of a banded system of an equitype linear equations.