Turyn-type sequences, , are quadruples of -sequences , with lengths , respectively, where the sum of the nonperiodic autocorrelation functions of and twice that of is a δ-function (i.e., vanishes everywhere except at 0). Turyn-type sequences are known to exist for all even n not larger than 36. We introduce a definition of equivalence to construct a canonical form for in general. By using this canonical form, we enumerate the equivalence classes of for . We also construct the first example of Turyn-type sequences .