Consider the \(n\)-dimensional boundary value problem \[ y'(x)=f(x,y)= \begin{cases} f_ 1(x,y)\quad &\text{if }a\leq x < s_ 1,\\ f_ 2(x,y)\quad &\text{if } s_ 1\leq x < s_ 2,\\ \vdots \\ f_{l+1}(x,y) \quad&\text{if }s_ l \leq x\leq b,\end{cases} \] when \(f_ i\) are smooth, with the boundary conditions \(R(y(a),y(b))=0\), together with certain switching and jump conditions. Since \(f\) is in general discontinuous at \(x=s_ i\), the solution may not be differentiable there, and the jump conditions may force it to have discontinuities at these points. The multiple shooting method reduces the problem to a Newton method for the solution of a related equation \(F(x)=0\), where \(F\) may have certain discontinuities which must be passed in the iteration process; this may prevent the Newton method from converging. The author develops a technique to avoid this difficulty by replacing \(F\) by a number of smooth functions which depend on the iteration process.