In the method in splicing in a continuous unwind, the surface speed of a new machine reel (R2) which is brought to the unwind and closed with a leading splice is accelerated in the initial acceleration to make the speed correspond to the speed of the old machine reel (R1) that is becoming empty, so that the fastening splice of the new machine reel can be joined to the web of the old machine reel. The loading affecting the leading splice and/or fastening splice of the new machine reel (R2) during the initial acceleration is reduced. The present invention also relates to an apparatus for implementing the method.