We　present　two　finite　difference　time　domain　methods　for　the　biharmonic　nonlinear　Schrödinger　equation　(BNLS)　by　reformulating　it　into　a　system　of　second-order　partial　differential　equations　instead　of　a　direct　discretization,　including　a　second-order　conservative　Crank–Nicolson　finite　difference　(CNFD)　method　and　a　second-order　semi-implicit　finite　difference　(SIFD)　method.　The　CNFD　method　conserves　the　mass　and　energy　in　the　discretized　level,　and　the　SIFD　method　only　needs　to　solve　a　linear　system　at　each　time　step,　which　is　more　efficient.　By　energy　method,　we　establish　optimal　error　bounds　at　the　order　of　O(h2+　τ2)　in　both　L2　and　H2　norms　for　both　CNFD　and　SIFD　methods,　with　mesh　size　h　and　time　step　τ.　The　proof　of　the　error　bounds　are　mainly　based　on　the　discrete　Gronwall’s　inequality　and　mathematical　induction.　Finally,　numerical　results　are　reported　to　confirm　our　error　bounds　and　to　demonstrate　the　properties　of　our　schemes.　©　2023,　The　Author(s),　under　exclusive　licence　to　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.