Multiple shooting for the solution of boundary value ODEs lends itself to parallel computation because the initial value ODEs that have to be integrated from one breakpoint to the next can be treated in parallel. A highly structured system of linear equations connecting these solutions must then be solved. The authors seek schemes that exploit the structure and are both stable and efficient on parallel computers. For separated boundary conditions, the normal equations for a least squares solution are block tridiagonal. They can be solved efficiently and stably in parallel with an odd-even reduction algorithm.