In　this　letter,　we　propose　a　two-stage　method　to　design　finite-length　puncturing　patterns　for　LDPC　codes　with　Hadamard　constraints.　At　the　first　stage,　we　propose　the　distribution　of　puncturing　patterns　and　develop　extrinsic　information　transfer　functions　for　distribution　optimization　in　terms　of　the　lowest　decoding　threshold.　At　the　second　stage,　we　analyze　the　iterative　update　process　of　a　Hadamard　check　node　(HCN)　and　find　that　the　Euclidean　distance　determines　the　reliability　of　its　output　extrinsic　information.　Based　on　this,　we　propose　a　greedy　algorithm　to　design　puncturing　patterns　to　maximize　the　number　of　punctured　variable　nodes　with　reliable　input　information.　Simulations　verify　the　good　performance　of　the　Hadamard-LDPC　code　with　our　designed　puncturing　patterns,　compared　to　the　5G　new　radio　LDPC　code　and　the　same　Hadamard-LDPC　code　with　other　puncturing　patterns.