We report here the discovery of an apparent excess of 2MASS M giant candidates with dereddened 0.85 < J-K_S < 1.2 spanning a considerably large area of the celestial sphere between, at least, $100degr < l < 150degr$ and $-20degr > b > -40degr$, and covering most of the constellations of Triangulum and Andromeda. This structure does not seem to be preferentially distributed around a clear core, but rather lies in a tenuous, clumpy cloud-like structure tens of kiloparsecs away. The reduced proper-motion diagram as well as spectroscopy of a subsample shows these excess stars to be real giants, not contaminating dwarfs. Radial velocity measurements indicate among those M giants the presence of a coherent kinematical structure with a velocity dispersion $sigma < 17$ km s$^{-1}$. Our findings support the existence of a quite dispersed stellar structure around the Milky Way that, due to its coreless and sparse distribution, could be part of a tidal stream or a new kind of satellite galaxy.