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In this paper, we propose a generalized formula for generating puncturing patterns for block-type low-density parity check (B-LDPC) codes with dual-diagonal parity structure. The proposed formula distributes punctured bits uniformly in the zigzag edge connections, as well as maximizes the minimum recovery speed and the reliability of each punctured node. Also, the proposed puncturing can be applied to any B-LDPC code with dual-diagonal parity structure and can provide efficient bitwise puncturing patterns even when the number of puncturing bits is not equal to an integer multiple of the block size. Simulation results show that the proposed punctured B-LDPC codes are better than existing punctured B-LDPC codes and even dedicated B-LDPC codes used in commercial standards.