Description: An innovative surface micromachining technique is described for the fabrication of closely-packed arrays of transition edge sensor (TES) x-ray microcalorimeters. This technique enables individual TES microcalorimeters to be suspended on a thin membrane for thermal isolation from the bath temperature. The TES detectors are fabricated from normal metal/superconductor bilayers with a transition temperature of around 0.1 K. The proposed surface micromachining technique will simplify the fabrication of closely-packed TES microcalorimeter arrays, which are needed for numerous applications in astronomical x-ray spectroscopy.