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We present a computational framework for analyzing brain hemispheric asymmetry without any kind of image flipping. In almost all previous literature, to perform brain asymmetry analysis, it was necessary to flip 3D magnetic resonance images (MRI) and establish the hemispheric correspondence by registering the original image to the flipped image. The difference between the original and the flipped images is then used as a measure of cerebral asymmetry. Instead of physically flipping MRI and performing image registration, we construct the global algebraic representation of cortical surface using the weighted spherical harmonics. Then using the inherent angular symmetry present in the spherical harmonics, image flipping is done by changing the sign of the asymmetric part in the representation. The surface registration between hemispheres and different subjects is done algebraically within the representation itself without any time consuming numerical optimization. The methodology has been applied in localizing the abnormal cortical asymmetry pattern of a group of autistic subjects using the logistic discriminant analysis that avoids the traditional hypothesis driven statistical paradigm.