Current techniques for transforming unforgeable signature schemes (the forged message has never been signed) to strongly unforgeable ones (the forged message could have been signed) require supplementary components to be added onto the original key pairs of the schemes. In addition, some of them can only be applied to a certain type of signature schemes. In this paper, we propose a new generic transformation technique which converts any unforgeable signature scheme into a strongly unforgeable one without modifying any component in the original key pair. This makes our technique especially compatible for practical use. Our technique is based on strong one-time signature schemes. We show that they can be constructed efficiently from any one-time signature scheme that is based on one-way functions. The performance of our technique also compares favorably with that of current ones. Besides, it is shown in this paper that our transformation (:an further be applied to schemes satisfying only a weak variant of unforgeability without any further modification. Furthermore, our technique can also be used for constructing strongly unforgeable signature schemes in other cryptographic settings which include certificateless signature, identity-based signature, and several others. To the best of our knowledge, similar extent of versatility is not known to be supported by any of those comparable techniques. Finally and of independent interest, we show that our generic transformation technique can be modified to an on-line/off-line signature scheme, which possesses a very efficient signing process.