Replacing exterior rotted joists on second story cantilevered deck

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We have an existing second story cantilevered deck off our master bedroom. The deck is 4 feet deep by 21 feet long. The exterior joists are rotted but the interior portion of the joists are fine. Since we can not replace the entire joist as a portion is under the bedroom floor, we are planning to remove the portion of the joists that are rotted (Exterior) and tie in the the existing joist 4 feet into the interior with an 8 foot joist that would allow the 4 feet for the exterior deck. Would this be a sound solution? What type of bolts should we use to tie into the existing joists. We will be using pressure treated wood.