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It is shown that the maximum cardinality of biangular lines is at least <jats:inline-formula><jats:alternatives><jats:tex-math>$$2(d-1)(d-2)$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>d<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>1<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                    <mml:mo>(<\/mml:mo>\n                    <mml:mi>d<\/mml:mi>\n                    <mml:mo>-<\/mml:mo>\n                    <mml:mn>2<\/mml:mn>\n                    <mml:mo>)<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and this result is sharp for <jats:inline-formula><jats:alternatives><jats:tex-math>$$d\\in \\{4,5,6\\}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>d<\/mml:mi>\n                    <mml:mo>\u2208<\/mml:mo>\n                    <mml:mo>{<\/mml:mo>\n                    <mml:mn>4<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>5<\/mml:mn>\n                    <mml:mo>,<\/mml:mo>\n                    <mml:mn>6<\/mml:mn>\n                    <mml:mo>}<\/mml:mo>\n                  <\/mml:mrow>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. 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