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Assume, I received a bitcoin in a regular transaction: T1. But I need to make MULTISIG transaction. so there should be at least n out of m signatures in new transaction :T3, to redeem it.

Am I right that to turn T1 to a MULTI-SIG one I need to do as follows:

1- I create new transaction T2, that points to T1, and includes all the m public keys and it pays to myself.

2- When I want to pay someone, I create new transaction: T3 (pointing to T2) includes n signatures and pays to another party.

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    There is no such thing as "multisig transaction". There is "multisig address". Transaction just a way to transfer bitcoin from one address(es) to another one(s)
    – amaclin
    Apr 11, 2017 at 12:12

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Yes, you are right. There are two ways of doing so:

You can create a multi-sig transaction as you mentioned, including a m-of-n script in which you will define the number of signatures (m) of the total n that will be necessary to redeem from the transition. The script structure from T2 will be:

ScriptPubKey: <m> <PubKey_1> <PubKey_2> ... <PubKey_n> n

And the redeem script from T3 will be:

ScriptSig: <Sig_1><Sig_2> ... <Sig_n>

Notice that, in order to be valid, the signatures in T3 must be in the same order as the public keys in T2.

On the other hand, you can encapsulate the multi-sig scripts mentioned avobe in a Pay-to-scriptHash, in that way the first transaction script (T2) will simpler, since it will be just a hash, and the transaction will look more similar to a traditional Pay-to-Publickey-hash.

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