Can we square off a equity futures contract intraday

Most certainly!

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You can square off all F & O contract intraday.

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Yes, you can.

But you should understand the SquareOff and Exercise are two different things.

When you are actually SquaringOff you are entering a counter (means opposite) trade, which actually closes your open position but not the contract itself. The obligation part for the contract to be exercised transfers from you to someone else.

Example, when you write options, you as a seller is supposed to pay the buyer when you are in loss during expiry. But when you are squaring off by entering a Buy position, the obligation to pay that buyer transfers to the person who sells you the square-off contract. The contract is still valid and the buyer can still exercise it on expiry day, but goodness not on you but someone else. (since you have squared off). May not be significant but hope you understand!