A restricted universal designated verifier signature scheme proposed by Huang et al., which is a variant of digital signatures, allows a signature holder to convince at most t designated verifiers.The signature will become publicly verifiable when the signature holder uses the signature for t+1 times.The applications of this type of signatures are expected to, for example, trial services or electronic votings on the internet. However, confirming process and universal opening are required in some situations. But both Huang et al.'s scheme as well as Laugullaumie et al.'s scheme do not support universal opening. In this paper, we propose a new restricted undeniable designated verifier signature scheme. Our scheme surpasses both Huang et al.'s scheme and Laugullaumie et al.'s scheme in the sense of universal opening.