We present first observations of a dome-shaped large-scale EUV coronal wave , recorded by the EUVI instrument onboard STEREO-B on January 17 , 2010 . The main arguments that the observed structure is the wave dome ( and not the CME ) are : a ) the spherical form and sharpness of the dome ’ s outer edge and the erupting CME loops observed inside the dome ; b ) the low-coronal wave signatures above the limb perfectly connecting to the on-disk signatures of the wave ; c ) the lateral extent of the expanding dome which is much larger than that of the coronal dimming ; d ) the associated high-frequency type II burst indicating shock formation low in the corona . The velocity of the upward expansion of the wave dome ( v \sim 650 km s ^ { -1 } ) is larger than that of the lateral expansion of the wave ( v \sim 280 km s ^ { -1 } ) , indicating that the upward dome expansion is driven all the time , and thus depends on the CME speed , whereas in the lateral direction it is freely propagating after the CME lateral expansion stops . We also examine the evolution of the perturbation characteristics : First the perturbation profile steepens and the amplitude increases . Thereafter , the amplitude decreases with r ^ { -2.5 \pm 0.3 } , the width broadens , and the integral below the perturbation remains constant . Our findings are consistent with the spherical expansion and decay of a weakly shocked fast-mode MHD wave .