In association with a computer system, a method and system for implementing a graphical dissolve effect of a first image into a second image displayed on a computer screen. The sequence in which each pixel comprising the first image is replaced with a corresponding pixel in the second image is determined mathematically such that the sequence appears random, thereby producing a dissolve effect that is visually pleasing. The sequence in which the pixels of a first image having a width and height of "w" and "h" pixels, respectively, are replaced is determined by first selecting a value for the variables p and m. The number p is a prime number and the number m is selected such that the numbers m, m.sup.2, m.sup.3, . . . , m.sup.p-1, when taken modulo p, yield a reordering of the numbers 1, 2, 3, . . . , p-1. A random number k.sub.0 is selected between 1 and p-1 and a number k is set equal to k.sub.0. A number j is then calculated according to the formula j=(w*h)+k-p. If j is non-negative, pixel number j in the first image is dissolved by replacing it with the corresponding pixel from the second image. A new number j is then calculated according to the formula j.sub.new =j-(p-1). If j is negative, a new value for the number k is calculated according to the formula k.sub.new =(k*m) mod p and then a new value of j is calculated according to the formula above using k.sub.new. The entire first 30 image is dissolved when the value of k.sub.new is equal to k.sub.0.