Although the photomultiplier-quactrant-sharing design introduced by our group for position sensitive detector blocks is very effective for reducing the cost of a high resolution PET camera, a section of the photomultiplier's sensitive windows at the edge of the block array remains unused. An elongated, asymmetrically offset position-sensitive detector block has been developed to utilize this unused area of the PMTs window. The block design employed asymmetric light partitions to achieve an evenly distributed two-dimensional position-decoding map. The block was divided into 7x8 elements. For this study, the dimensions of each detector element were 2.66 x 3.05 mm with a depth of 18 mm. This detector design is applicable to any camera using the PMT quadrant-sharing detector design, such as the Variable Field Prototype PET Camera developed at M. D. Anderson Cancer Center (MDAPET) and the Siemens/CTI LSO cameras. A second improvement incorporated into the detector design was the replacement of the saw-cut grooves in the detector blocks by painted masks. The application of the present block design to a clinical high resolution camera expands the axial field-of-view, which, when combined with the gapless block design used in this study, increases the coincidence detection efficiency of the camera by factor of about 2.9 in 3-D data acquisition.