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Rare decays of the Higgs boson into a pair of diquarks <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mi>c</mi><mo>(</mo><mi>b</mi><mi>b</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>c</mi><mo>¯</mo></mover><mover accent="true"><mi>c</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mover accent="true"><mi>b</mi><mo>¯</mo></mover><mover accent="true"><mi>b</mi><mo>¯</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula> are studied within the perturbative Standard Model and relativistic quark model. The relativistic corrections determined by the relative motion of quarks are calculated using the production amplitude and the diquark wave functions. Numerical values of the decay widths of the Higgs boson into a baryon pair <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mi>c</mi><mi>q</mi></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>b</mi><mi>b</mi><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mover accent="true"><mi>c</mi><mo>¯</mo></mover><mover accent="true"><mi>c</mi><mo>¯</mo></mover><mover accent="true"><mi>q</mi><mo>¯</mo></mover></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mover accent="true"><mi>b</mi><mo>¯</mo></mover><mover accent="true"><mi>b</mi><mo>¯</mo></mover><mover accent="true"><mi>q</mi><mo>¯</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula> are obtained.