  We consider a texture for the neutrino mass matrix characterized by one
vanishing $2\times2$ subtrace. We analyze phenomenologically and analytically
all the six possible patterns, and show that all non-singular ones are able to
accommodate the experimental bounds, whereas singular patterns allow only for
four inverted-hierarchy type textures. We then present some possible
realizations of this texture, within seesaw scenarios, either directly or
indirectly by relating it to zero-textures.
