Random number generation is one of the important issues of cryptography. Based on the efficient Mycielski predictor, we propose a new random number generation algorithm, denoted by Anti-mycielski, which generates a new data at the end of a sequence by making it orthogonal to the prediction. By taking the initial sequence as a key, it is possible to use the algorithm for encryption purposes by masking. The algorithm works on binary sequences and each 8 bit block is converted to integers. Since the complexity of the algorithm is of non-polynomial order, it is necessary to occasionally chop the history of the predictor. The effect of history length and the length of the key is analyzed in terms of the quality of the generated random sequence.