Can a husband do second marriage leaving his first wife without any proper reason

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad sallallaahu`alayhi wa sallam is His slave and Messenger.

It is permissible for a man to marry a second, a third and a fourth woman. There are no specific conditions for this permissibility, such as a shortcoming or a defect in the first wife, except for the condition of treating justly. For more benefit, please refer to Fatwa 172567.

As for the husband leaving his first wife after marrying another woman; if by "leaving" you mean not staying overnight with her, or not spending on her, and the like, then this is forbidden and not permissible. There is a stern warning issued to the one who does not treat his wives equally.

And if by "leaving" is meant divorce, if he has an excuse, such as if she mistreats him and so on, then divorcing her in a such case is permissible, but if he divorces for no reason and the situation between them is upright, then some scholars are of the view that divorce is disliked in this case, and others are of the view that it is forbidden.

Allah knows best.