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The ordinary twin paradox is a problem of ageing of two twin observers A and B, B travels with a relativistic speed and returns back to A where A is at rest. According to each twin's calculation, if each considers itself at rest, the other would be younger at the end of the trip. This is paradoxical, in fact the paradox appears due to the accelerating of the travelling twin (B) and so that B will be younger at the return point. This paradox has been resolved by T. Dray by doing the calculation in a closed cylindrical universe, were the acceleration problem has been resolved for the travelling twin. This means that the travelling (faster) twin will be younger no matter which twin performed the calculation. In the present calculation we have shown if both twins are travelling with a relativistic speed in such universe and the faster twin (B) made the calculations. The result will always shows that the faster twin will have less proper time. This result is consistent with that of T. Dray, when one twin is at rest and other is moving.