The present fastener is of the general type shown in U.S. Pat. Nos. 4,021,891; 4,453,294; and 5,274,889. Such magnetic fasteners includes cooperating female and male member assemblies. The female member includes a permanent magnet, a ferromagnetic member at one of its poles and appropriate cover means for protectively enclosing the permanent magnet and controlling the magnetic flux paths. The male member assembly includes a cooperating ferromagnetic member which will be magnetically attracted to the female member assembly. To provide for proper positioning and centering of the inter-engaged male and female member assemblies, the permanent magnet of the female assembly includes a central opening for receiving, and appropriately positioning, a projecting ferromagnetic portion of the male member assembly. In order to (a) appropriately protect the magnet from damage, (b) provide an aesthetically pleasing overall surface appearance, and (c) of particular importance, control the flux paths, it has been the general practice to enclose the female member assembly in external metal or other surface coverings which may include ferromagnetic and non-ferromagnetic portions. Such enclosure members may typically be formed of brass or brass plated non-ferromagnetic metal. The particular selection and configuration of the ferromagnetic and non-ferromagnetic portions has varied in accordance with the particular requirements and design of the particular fastener. By and large, the prior art magnetic fasteners have generally included a cover enclosure which extends over the major surface of the permanent magnet and which is generally visible on the surface of the handbag or accessories to which the female portion is affixed. Although widely successful, fasteners of this type may cause some erasure of magnetic encoding on credit cards or the like which are stored in handbags. Although some prior workers have attempted to address this problem, the solutions have not met with wide commercial acceptance.