In this paper we give a new definition of harmonic curvature functions in terms of B2 and we define a new kind of slant helix which we call quaternionic B2−slant helix in 4−dimensional Euclidean space E 4 by using the new harmonic curvature functions. Also we define a vector field D which we call Darboux quaternion of the real quaternionic B2−slant helix in 4−dimensional Euclidean space E 4 and we give a new characterization such as:where H2, H1 are harmonic curvature functions and K is the principal curvature function of the curve α.

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