Counterflow plate-fin heat exchanger with extended header fin

A plate-fin heat exchanger (18) includes a stacked array of cells (22). Each cell (22) includes top and bottom sheets (58,62) defining manifolds (26,30) and header finned members (66,70) disposed between the top and bottom sheets (58,62). The top and bottom sheets (58,62) include substantially planar portions (82), diverging portions (86) angled with respect to the planar portions (82), and divergence edges (90) defined between the planar (82) and diverging (86) portions. The header finned member (70) extends beyond the divergence edges (90) of the top and bottom sheets (58,62) and is supported in cantilevered fashion within the manifold.