A　sufficient　and　necessary　criterion　for　separability　of　bipartite　quantum　states　is　presented.　We　construct　a　class　of　mixed　states　in　2　circle　times　k　quantum　systems　and　in　3　circle　times　k　quantum　systems,　respectively　and　show　that　these　states　are　separable　if　and　only　if　they　are　positive　partial　transpositions.