The state’s highest court on Wednesday threw out the conviction of a former Wareham man who was found guilty in 2014 of raping his daughter more than 30 years earlier, when she was between the ages of 4 and 6.

In a unanimous ruling, the Supreme Judicial Court said Robert E. White’s child rape conviction in Plymouth Superior Court could not stand because of an issue related to the statute of limitations.

Under state law, defendants can be convicted of child rape for incidents that occurred more than 27 years prior to indictment only if there is corroborating evidence, in addition to the alleged victim’s testimony.

In White’s case, his daughter testified at trial to “various incidents of rape,’’ some that occurred before Oct. 3, 1981, and some that happened after that date, the ruling said.

The SJC found that prosecutors failed to provide required corroborating evidence for the incidents before Oct. 3, 1981, and the jury may have based its guilty verdict solely on those earlier encounters, so the conviction must be vacated.

Justice Barbara A. Lenk wrote in the 36-page ruling that if prosecutors retry White, they can only charge the alleged acts that occurred after Oct. 3, 1981.

His daughter testified at trial to repeated assaults and said White would “smack’’ her whenever she resisted, telling her that “this is how a father shows his daughter love, that we have a secret and I can’t tell,’’ the ruling said

White countered that the daughter’s “memories of abuse were false, being the result of suggestive questioning’’ by his ex-wife, the ruling said.

The jury acquitted White of charges that he raped and assaulted the woman’s brother. White is currently incarcerated at a state prison in Gardner.

Lenk conceded in the ruling that there is “a high bar for prosecuting sexual offenses against children that are alleged to have occurred many years before,’’ adding that the legal threshold is not insurmountable.

Travis Andersen can be reached at travis.andersen@globe.com.