Hough Transformation (HT) is an efficient method to detect straight lines in digital pictures. In the conventional HT, pixel contiguity is not taken into account, and this leads to the following drawbacks: (1) actual length of line segments cannot be computed; (2) colinear line segments cannot be distinguished; and (3) very often, false lines are detected and short lines go undetected. This paper proposes a modified Hough Transformation which performs contiguity check in a simple and efficient way. A systolic architecture that implements this modified transform is presented. The systolic array takes the bit-map of the binary picture as input and processes one row/column of pixels concurrently. The area-time complexity of the proposed architecture is shown to be superior to the conventional sequential algorithm. Preliminary simulation results are presented.