DescriptionStencil computations represent a very common class of nested loops in scientific and engineering applications. The exhaustively studied tiling is one of the most powerful transformation techniques to explore the data locality and parallelism. Unlike previous work, which mostly blocks the iteration space of a stencil directly, this paper proposes a novel two-level tessellation scheme. A set of blocks are designed to tessellate the spatial space in various ways. The blocks can be processed in parallel without redundant computation. This corresponds to extending them along the time dimension and can form a tessellation of the iteration space. Experimental results show that our code performs up to 12% better than the existing highly concurrent schemes for the 3d27p stencil.