Blowing up projectively normal space curves and very ample divisors

Let C subset of P-3 be a projectively normal curve and pi : X(C) --> P-3 th e blowing-up of C, E the exceptional divisor of pi and H is an element of P ic(X(C)) the total transform of the hyperplane line bundle. Let H(C, t) be the Hilbert function of C and Delta H-2 its second difference function. Let sigma be the minimal integer such that Delta H-2(C, sigma) = 0. Here we pr ove that is C has no sigma -secant line, then /aH - E/ is very ample.