While traditional construction of binary polar codes with Arikan’s 2×2 kernels is proved to achieve capacity, its performance under reasonable decoding complexity is far from satisfactory. It is conjectured that by substituting a larger kernel, one may improve scaling and error exponents, as merits for the finite-length performance. In this work, we present heuristic approaches in construction of such kernels. An efficient decoding algorithm for these kernels is also proposed.