From Wikipedia, a rhombus is a special parallelogram and would not fit the question:

"In any rhombus, opposite sides are parallel. Thus, the rhombus is a special case of the parallelogram."

A diamond in the shape of a kite would fit the question. A quadrangle with 2 pairs of equal sides but not a parallelogram. Thanks dy2147...and everyone else who answered. Guess I'm not smarter than a 4th grader. LOL

http://en.wikipedia.org/wiki/Kite_(g...