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In a paramagnetic state of a hyperkagome lattice antiferromagnet Mn_{3}RhSi, magnetic diffuse scattering by magnetic short-range order is observed over a wide temperature range of approximately 500 K above the Néel temperature of 190 K. We have studied the magnetic excitation with a single crystal in a wide energy range from 0.3 to 140 meV by inelastic neutron scattering, where the prominent inelastic neutron-scattering signal is observed at Q=(2,0,0). The inelastic scattering intensity integrated for two of twelve magnon modes leads to a localized magnetic moment of about 5 μ_{B} per Mn site, although the long-range ordered magnetic moment is only 2.61 μ_{B} at 4 K. The result suggests that a large part of the magnetic moment does not order in Mn_{3}RhSi, possibly due to the geometrical spin frustration of the hyperkagome lattice.