A modification of the normalized Fry method is developed to avoid the problems associated with approximating non-elliptical grains by best-fit ellipses. This modified method is a more general approach for constructing a normalized Fry plot and determining the orientation and axial ratio of the fabric ellipse. Grains can be approximated by any shape as long as the center and area of each grain can be determined. Irregular polygons work particularly well since they can be used to approximate both elliptical and non-elliptical grains. Once the center and area of each grain in an aggregate is calculated, existing methods can be used to construct a normalized Fry plot. Determining the fabric ellipse, however, requires a new approach. A circular grid is used to find points on the ring of maximum point density along a series of radial vectors. The least-squares best-fit ellipse calculated through these points gives an initial estimate of the fabric ellipse. An iterative approach is taken, using the fabric estimate to calculate a plane strain irrotational inverse deformation matrix which, in turn, is used to unstrain grain centers. The newly determined centroids are used to calculate a new fabric ellipse. This process is repeated until the axial ratio of the remaining fabric ellipse is 1.00. The fabric ellipses for each stage are combined to calculate the total fabric ellipse. Tests of this method using computer generated data sets of elliptical and non-elliptical grains show a strong correlation of measured fabric with known artificially imposed fabric.