word order 你不打电话给他 / 你不给他打电话
In a book I'm reading/studying there is this sentence: 你不打电话给他也没关系，他已经知道了。
My question is, would 你给他不打电话..... also be correct?
Is there a rule for word order in such cases?

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你给他不打电话 is incorrect. It can be understandable by native speaker.Obviously this is influenced by English.
It can be 你给不给他打电话都没关系。It's similar with 你不打电话给他也没关系。I guess this is word order you mentioned。
BTW,rule of word order can't tell with concise words，it's complicated for non-professionals like me.

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你给他不打电话，很奇怪，听起来

No rule

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That guy has the right answer. I am also non-professional but I  think he is correct. 给他不打电话is understandable for us native speakers but it's incorrect.

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word order is key to Mandarin, it is a big grammar topic, hard to explain here. 你不给他打电话 is correct, while the other is heard quite often as well, 给+x is quite a special case, could be the impact from English etc.

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Short answer: no. But you could say "不给她打电话", which I think is more proper.