The spatial components of the autocorrelation function of noninteracting dipoles are analytically obtained in terms of rotational Brownian motion on the surface of a unit sphere using multi-level jumping formalism based on Debye's rotational relaxation model, and the rotational relaxation functions are evaluated.PACS numbers: 77.22. Gm, 05.40.Jc, Rotational Brownian motion and rotational relaxation phenomena has received considerable interest in the literature for a long time. Historically, the problem of isotropic rotational Brownian motion arose in connection with the work of Purcell on spin relaxation in systems with more than two spins in the same molecule. The dynamics of rotational Brownian motion of a sphere around a given axis was discussed briefly by Einstein [1] in one of his early papers. Later, Debye [2] proceeded by extending Einsteins treatment of the translational Brownian motion to rotational Brownian motion of noninteracting permanent dipoles in the presence of an external timevarying field and solving the appropriate Fokker-Planck equation. Here that equation is the Smoluchowski equation, which is an approximate Fokker-Planck equation in the space of angular coordinates for the distribution function of the orientations of the dipoles on the surface of the unit sphere when the influence of the inertia of the molecules on the relaxation process is ignored. Following years many generalizations of Debye model have been extensively studied [3,4,5,6,7,8,9,10,11]. However, Debye theory cannot explain relaxation phenomena in strongly interacting systems. The relaxation behavior in strongly interacting systems such as amorphous polymers, spin glasses, glass forming liquids, etc., deviates considerably from the exponential (Debye) pattern Φ ∼ exp [−t/τ ] and is characterized by a broad distribution of relaxation times. The relaxation in strongly interacting systems obey to the stretched exponential relaxation function experimentally Φ ∼ exp [−(t/τ ) α ] with 0 < α < 1, which often referred to as the KohlrauschWilliam-Watts (KWW) function [12,13].In this Letter our aim is to obtain rotational relaxation function in terms of autocorrelation function of rotational Brownian motion using multi-level jumping process (MJP) formalism based on historical Debye rotational relaxation scenario. The MJP is the generalization of the two-level jumping process (TJP) formalism. The TJP and MJP have been used to obtain the relaxation function [14,15,16,17]. Recently, the non-exponential relaxation function in complex systems has been obtained using MJP formalism [18]. * Electronic address: ekrem.aydiner@deu.edu.tr Autocorrelation function φ is simply given by( 1) where µ(0) and µ(t) denote values of fluctuation variable µ, i.e. dipole, at time zero and the same variable at a later time t, respectively. Physically, it measures the time over which the variable µ retains its own memory until this memory is averaged out by statistical randomness.If it is assumed that the external field has been applied in the z-direction, the...