  In [18], L. R. Pears proved that Bertrand curves in E-n(n > 3) are degenerate
curves. This result restate in [16] by Matsuda and Yorozu. They proved that
there is no special Bertrand curves in E-n(n > 3) and they define new kind of
Bertrand curves called (1, 3)-type Bertrand curves in 4-dimensional Euclidean
space. In this study, we define a quaternionic Bertrand curve ?(4) in Euclidean
space E4 and investigate its properties for two cases. In the first case; we
consider quaternionic Bertrand curve in the Euclidean space E4 for r-K = 0
where r is the torsion of the spatial quaternionic curve ?; K is the principal
curvature of the quaternionic curve ?(4): And then, in the other case, we prove
that there is no quaternionic Bertrand curve in the Euclidean space E4 for r -
K = 0: So, we give an idea of quaternionic Bertrand curve which we call
quaternionic (N - B2) Bertrand curve in the Euclidean space E4 by using the
similar method in [16] and we give some characterizations of such curves.
