ず is the classical version of the negative ending ない. It is often used in writing and in other grammatical structures. For group 1 and 2 verbs we simply replace ない with ず as per the following table:

English Dictionary Negative ず Form
to go かない かず
to swim およ およがない およがず
to go home かえ かえらない かえらず
to say わない わず
to think かんがえる かんがえない かんがえず

For group 3 verbs.

 English Dictionary Negative ず Form
to do する しない せず
to come 来る 来ない 来ず

To create the ないで te form we simply add に.

あまり相手あいて気持きもちを考慮こうりょせずにきびしい言葉ことばけた。
Without much considering the other person’s feelings he hurled some harsh words.
かんがえずに旅行りょこう予約よやくれる。
To book a holiday without hesitation.
予約よやくせずにおみせく。
To go to a restaurant without making a reservation.
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