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Malonaldehyde is an open 5-membered ring molecule which exhibits interesting quantum-mechancial effects due to tunnelling of one of its protons. This results in a 21 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ tunnelling-splitting in the ground vibrational state, which has been well-studied by microwave spectroscopy \textbf{106} (1984) 2265-2267; T. Baba, T. Tanaka, I. Morino, K. M. T. Yamada and K. Tanaka, \textit{J. Chem. Phys.} \textbf{110} (1999) 4131-4133.}. We have taken far-infrared Fourier transform spectra of malonaldehyde at the Canadian Light Source synchrotron, and have recorded a number of rotation-vibration fundamental bands between 100-1000 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ at 0.00096 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ resolution. The data permit us to determine with high precision the changes in the tunnelling-splitting induced by vibrational excitation. We have also observed spectra at 240 and 219 cm$\mathrm{<mrow\; data-mjx-texclass="ORD">-1</mrow>}$ that appear to be transitions from the two components of the ground vibrational state to a common upper state that is not mentioned in conventional vibrational analyses of malonaldehyde \textbf{290} (2003) 15-25.}. We will offer suggestions as to the nature of the newly-observed state.