Directional solidification experiments were carried out for succinonitrile-1.0 wt pct acetone alloy with the orientation of dendritic arrays being not parallel to the direction of the temperature gradient. Experimental results show that there exists an allowable range of primary dendritic spacing under a given growth condition.The average primary spacing depends not only on the current growth conditions but also on the way by which the conditions were achieved. The upper limit of the allowable range becomes smaller in comparison with that with direction of dendrite arrays parallel to the direction of the temperature gradient, which means that the history-dependence of dendritic growth is weaker under this condition. The lower limit obtained is compared with a self-consistent model, which shows a good agreement with experimental results.