A stable second order Cartesian grid finite difference scheme for the solution of Maxwells equations is presented. The scheme employs a staggered grid in space and represents the physical location of the material and metallic boundaries correctly, hence eliminating problems caused by staircasing, and, contrary to the popular Yee scheme, enforces the correct jump-conditions on the field components across material interfaces. To validate the analysis several test cases are presented, showing an improvement of typically 1-2 orders of accuracy at little or none additional computational cost over the Yee scheme, which in most cases exhibits first order accuracy.