The fault diagnosis for maintenance of machines operating in variable conditions requires special dedicated methods. Variable load or temperature conditions affect the vibration signal values. The article presents a new approach to diagnosing rotating machines using an artificial neural network, the training of which does not require data from the damaged machine. This is a new approach not previously found in the literature. Until now, neural networks have been used for machine diagnosis in the form of classifiers, where data from individual faults were required. A new diagnostic parameter rDPNS (Relative Differences Product of Network Statistics) as a function of the machine's shaft order was proposed as a kind of new order spectrum independent of the machine's operating conditions. The presented work analyses the use of the proposed method to diagnose misalignment and unbalance. The results of an experiment carried out in the laboratory demonstrated the effectiveness of the proposed method.