One of the central issues in the cuprates is to clarify the interplay between magnetism and superconductivity. Intensive efforts have been devoted toward the magnetic resonance and the seemingly universal hourglass-like magnetic dispersion near the antiferromagnetic wave-vector (QAF). Our recent neutron scattering work on HgBa2CuO4 (Hg1201) has revealed two novel magnetic excitations in the pseudogap state. Unlike the more conventional magnetic excitations, these excitations are nearly dispersionless and exist throughout the entire Brillouin zone. The hourglass dispersion has yet to be conclusively observed in Hg1201. Initial results on new very underdoped sample(Tc=50K) show a resonance at 32 meV and hints of an hourglass-like dispersion emanating from that point. Here we propose to further study our underdoped Hg1201 sample to firmly establish the existence and properties of the hourglass dispersion in Hg1201. We will also search for the pseudogap state novel excitations in this very underdoped Hg1201 sample.