about the word "that"

[Jakeboy]

He reminded them that there were no trains after midnight.
The word "that" in the sentence above can drop off? For example: He reminded them there were no trains after midnight. Is the sentence correct?
Thank you in advance!

 

[David L.]

Yes, the sentence is correct.
'that' can be omitted where it is used as a conjunction and introduces a subordinate clause, as in : "She said (that) she was satisfied."
'that' can also be dropped in a relative clause where it is the object of the clause, as in : "The book (that) I've just written."
'that' MUST be used when it is the subject of the relative clause, as in : "The company that employs Jack."