Abstract: Cloth animation is an important area of computer graphics due to its numerous applications. However, so far a fast moving cloth with multiple wrinkles has been difficult to animate because of the cloth clump problem. Cloth clumps are the frozen areas where cloth pieces are clustered unnaturally --- an obstacle in making a realistic cloth animation. Hence we present a novel cloth collision resolution algorithm that prevents clump formation during fast cloth motions. The goal of our resolution algorithm is to make cloth move swiftly without having any unnatural frozen cloth clumps, while preventing any cloth-cloth and rigid-cloth penetrations at any moment of a simulation. The non-penetration status of cloth is maintained without the formation of cloth clumps regardless of the speed of cloth motion. Our algorithm is based on a particular order that we found in the resolution of cloth collisions, and can be used with any structural modeling approaches such as spring-masses or finite elements. This paper includes several realistic simulation examples involving fast motions that are clump-free.