In each step of quasi-Newton methods an improved approximate solution \(x_ k\) is determined together with a new approximation \(B_ k\) of the derivative f'. Specifically, Broyden's method yields an update \(B_{k+1}\) which is the solution of the minimum problem: \(\min \{\| B-B_ k\|_ F: Bs_ k=y_ k\}.\) Here \(y_ k\) and \(s_ k\) are vectors which are computed during the iteration. If there is some extra information on the structure of the derivatives, one may consider the problem \(\min \{\| B-B_ k\|_ F: Bs_ k=y_ k,\) B satisfies extra conditions\(\}\). In the present paper this is done for the case that upper and lower bounds are known for the entries of the Jacobian matrix. It is shown that the known local convergence properties are not lost when the update is performed subject to the extra conditions.