Based on Shamir's threshold scheme and the RSA cryptosystem, a new secret sharing scheme for the general access structure is proposed in this paper. In this scheme, each participant's secret shadow is selected by the participant himself and the dealer need not deliver any secret information to each participant, and thus a secure channel between them is unnecessary. The shadows do not need to be changed when the shared secret is renewed, the access structure is altered, or old participants are deleted/new participants are added. All these shadows are shorter than or as short as the shared secret. Each participant shares many secrets with other participants by holding only one shadow, and in the recovery phase each participant is allowed to check whether another participant provides the true information or not. The security of this scheme is the same as that of Shamir's threshold scheme and the RSA cryptosystem. Analyses show that this scheme is a computationally secure and efficient scheme.