Bridges of Königsberg

Königsberg is divided by a river into four land areas: a north bank, a south bank, and two islands. Seven bridges connect them. The larger island has two bridges to the north bank, two to the south bank, and one to the smaller island. The smaller island also has one bridge to each riverbank. A traveler may begin on any land area and finish anywhere. Land areas may be visited more than once, but each bridge must be crossed exactly once, without swimming, jumping, or retracing a bridge. Can such a walk be made?