A new additional melting peak is formed on the DSC thermogram as a result of preexpansion of poly(propylene-co-ethylene-co-1-butene) (terpolymer). The new melting peak appears at similar to 152 degrees C, which is similar to 12 degrees C higher than the tail end temperature (offset temperature) of the pristine terpolymer to exhibit a double melting peak. The origin of the new melting peak is traced to melting and recrystallization of less perfect crystals of the terpolymer at the preexpansion temperature, which situates usually between the onset and the offset temperature of the melting peak, contrary to the common presumption that the less perfect crystals are melted leaving the more perfect crystals intact during the preexpansion step and that the peak at similar to 152 degrees C comes from melting of the more perfect crystals. The higher the temperature to which the terpolymer was heated above the offset temperature, the longer time of annealing was required at the preexpansion temperature for the new peak to appear. Once the terpolymer was completely melted by heating to 175 degrees C, at least 24 h of annealing was needed to show up the new melting peak, indicating that crystallization with homogeneous nucleation takes place much more slowly than that with self-nucleation.