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This paper demonstrates a super-resolution method for improving the resolution in clinical positron emission tomography (PET) scanners. Super-resolution images were obtained by combining four data sets with spatial shifts between consecutive acquisitions and applying an iterative algorithm. Super-resolution attenuation corrected PET scans of a phantom were obtained using the two-dimensional and three-dimensional (3-D) acquisition modes of a clinical PET/computed tomography (CT) scanner (Discovery LS, GEMS). In a patient study, following a standard 18F-FDG PET/CT scan, a super-resolution scan around one small lesion was performed using axial shifts without increasing the patient radiation exposure. In the phantom study, smaller features (3 mm) could be resolved axially with the super-resolution method than without (6 mm). The super-resolution images had better resolution than the original images and provided higher contrast ratios in coronal images and in 3-D acquisition transaxial images. The coronal super-resolution images had superior resolution and contrast ratios compared to images reconstructed by merely interleaving the data to the proper axial location. In the patient study, super-resolution reconstructions displayed a more localized 18F-FDG uptake. A new approach for improving the resolution of PET images using a super-resolution method has been developed and experimentally confirmed, employing a clinical scanner. The improvement in axial resolution requires no changes in hardware.