A blind signature provides perfect confidentiality to a message and signature pair. Due to this feature, the blind signature has one downside; the signer can not assure himself that the blinded message accurately contains the information he desires. In a practical sense, it is essential for the signer to include some term of validity in the signing message to prevent abusing. Of course the term must not violate the confidentiality of the message. This paper discusses partial blinding of a signed message. We consider RSA and it is proved that forging the proposed scheme by multiple signing is as difficult as breaking RSA. The strategy can be also applied to those blind signature schemes that use a trapdoor function. An electronic cash system is shown as an application of the proposed scheme. Unlike most privacy-protected electronic cash system, it successfully minimizes the growth of the bank's database.