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Excited states in 212Po were populated by alpha transfer using the 208Pb(18O,14C) reaction, and their deexcitation gamma rays were studied with the Euroball array. Several levels were found to decay by a unique E1 transition (Egamma<1 MeV) populating the yrast state with the same spin value. Their lifetimes were measured by the Doppler-shift attenuation method. The values, found in the range 0.1-1.4 ps, lead to very enhanced transitions, B(E1)=2x10(-2)-1x10(-3) W.u. These results are discussed in terms of an alpha-cluster structure which gives rise to states with non-natural-parity values, provided that the composite system cannot rotate collectively, as expected in the "alpha+208Pb" case. Such states due to the oscillatory motion of the alpha-core distance are observed for the first time.