The problem of constructing an n by n Jacobi matrix J with prescribed spectrum {λi}n1, such that the submatrix J(ρ), obtained from J by deleting its ρth row and column, also has a prescribed spectrum {𝜇i}n-11 is studied. The cases ρ=1 and ρ=n are well known. For the case 2 ≤ ρ ≤ n-1 it is shown that the problem has a unique solution under the condition λi < 𝜇i < λi+1, i=1, 2, . . . , n-1.