Oligomers with $alpha$-aminooxy acids are reported to form very stable turn and helix structures, and they are supposed to be useful peptidomimetics for drug design. A recent report suggested that homochiral oxa-peptides form a strong eight-member-ring structure by a hydrogen bond between adjacent aminooxy-acid residues in a $CDCl_3$ solution. In order to design an $alpha$-MSH analog with a stable turn conformation, we synthesized four tetramers and one pentamer, based on $alpha$-MSH sequence, and determined the solution structures of the molecules by two-dimensional NMR spectroscopy and simulated annealing calculations. The solution conformations of the three peptidomimetic molecules (TLV, TDV, and TLL) in DMSO-$d_6$ contain a stable 7-membered-ring structure that is similar to a $gamma$-turn in normal peptides. Newly-designed tetramer TDF and pentamer PDF have a ball-type rigid structure that is induced by strong hydrogen bonds between adjacent amide protons and carbonyl oxygens. In conclusion, the aminooxy acids, easily prepared from natural or unnatural amino acids, can be employed to prepare peptidomimetic analogues with well-defined turn structures for pharmaceutical interest.