Aperture synthesis observations of two HI cloud complexes located in the periphery of the Virgo galaxy cluster are presented . These low HI-mass clouds ( M _ { HI } < 10 ^ { 9 } ) are seen projected on the M region of the western Virgo cluster , where the galaxy population is thought to lie behind the main A cluster surrounding M87 . The kinematic measurements of both unresolved Arecibo and resolved VLA-C observations are in good agreement . The HI detections can not be identified with any optical , IR , or UV emission from available archival imaging . They are inert at these wavelengths . The HI masses of the individual VLA detections range from 7.28 \leq log ( M _ { HI } ) \leq 7.85 . The total dynamical mass estimates are several times their HI content , ranging from 7.00 \leq log ( M _ { dyn } ) \leq 9.07 , with the assumption that the clouds are self-gravitating and in dynamical equilibrium . We report the observed parameters derived from the VLA observations . One of these HI clouds appears to be the most isolated optically inert detection observed in the outer reaches of Virgo . Accepted for publication in The Astrophysical Journal .