This paper presents a search for exotic decays of the Higgs boson into a pair of new pseudoscalar particles, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>H</a:mi><a:mo stretchy="false">→</a:mo><a:mi>a</a:mi><a:mi>a</a:mi></a:mrow></a:math>, where one pseudoscalar decays into a <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi>b</d:mi></d:math>-quark pair and the other decays into a <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>τ</f:mi></f:math>-lepton pair, in the mass range <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mn>12</h:mn><h:mo>≤</h:mo><h:msub><h:mi>m</h:mi><h:mi>a</h:mi></h:msub><h:mo>≤</h:mo><h:mn>60</h:mn><h:mtext> </h:mtext><h:mtext> </h:mtext><h:mi>GeV</h:mi></h:math>. The analysis uses <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>p</j:mi><j:mi>p</j:mi></j:math> collision data at <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:msqrt><l:mi>s</l:mi></l:msqrt><l:mo>=</l:mo><l:mn>13</l:mn><l:mtext> </l:mtext><l:mtext> </l:mtext><l:mi>TeV</l:mi></l:math> collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mn>140</n:mn><n:mtext> </n:mtext><n:mtext> </n:mtext><n:msup><n:mi>fb</n:mi><n:mrow><n:mo>−</n:mo><n:mn>1</n:mn></n:mrow></n:msup></n:math>. No significant excess above the Standard Model (SM) prediction is observed. Assuming the SM Higgs boson production cross section, the search sets upper limits at 95% confidence level on the branching ratio of Higgs bosons decaying into <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:mi>b</p:mi><p:mover accent="true"><p:mi>b</p:mi><p:mo stretchy="false">¯</p:mo></p:mover><p:msup><p:mi>τ</p:mi><p:mo>+</p:mo></p:msup><p:msup><p:mi>τ</p:mi><p:mo>−</p:mo></p:msup></p:math>, <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mi mathvariant="script">B</t:mi><t:mo stretchy="false">(</t:mo><t:mi>H</t:mi><t:mo stretchy="false">→</t:mo><t:mi>a</t:mi><t:mi>a</t:mi><t:mo stretchy="false">→</t:mo><t:mi>b</t:mi><t:mover accent="true"><t:mi>b</t:mi><t:mo stretchy="false">¯</t:mo></t:mover><t:msup><t:mi>τ</t:mi><t:mo>+</t:mo></t:msup><t:msup><t:mi>τ</t:mi><t:mo>−</t:mo></t:msup></t:math>), between 2.2% and 3.9% depending on the pseudoscalar mass. © 2024 CERN, for the ATLAS Collaboration 2024 CERN