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In this letter, we propose a method to design an orthonormal two channel cyclic filterbank (CFB) with real analysis and synthesis filters hating linear phase. This is particularly significant, since it is not possible to realize regular two- channel linear phase orthogonal filterbanks (unless the filters are two-tap). The lowpass filter of the FB is obtained as a spectral factor of a zero phase Nyquist(2) filter, which is optimized. We show that the CFB design is computationally less demanding as compared to the noncyclic case, and it may be possible to get better filters. We design the CFB for a particular case and show that this filterbank is not a noncyclic orthogonal filterbank.