One way to build a satellite that will not leave debris in space is to collect the satellite after it is no longer useful. Another strategy could be to build the satellite out of material that will burn up or otherwise disintegrate in the atmosphere of outer space.
Most of the materials currently used to build satellites however are going to float around in space until they either crash back into earth or another planet. There is also growing concern that space debris is going to start morphing together and creating an even greater danger for space travel or for debris that re-enters the earth's atmosphere.