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The Archbishop of Canterbury has acknowledged how the rejection of women bishops has damaged the Church, in his final Christmas Day sermon.

The Most Reverend Rowan Williams said the aftermath of last month's General Synod vote had been "deeply painful".

He also said he had met many people during his 10 years in his role who had suffered violence and loss.

"Forgiveness and rebuilding relations" are key challenges for everyone, he said at Canterbury Cathedral.

His replacement in the Church of England's top role will be the Bishop of Durham, the Rt Rev Justin Welby, who will take over in the spring.

Dr Williams, along with Bishop Welby and the Archbishop of York John Sentamu, tweeted sections of their Christmas sermons on the micro-blogging site Twitter.

The senior clerics were expected to be joined by about 16,000 Church members tweeting on Christmas morning.

During his sermon, Dr Williams acknowledged that the recent vote not to allow women bishops in the Church had damaged its credibility.

However, he said that according to recent census results, 59% of people still identified themselves as Christian, and believers should not lose heart.

"In the deeply painful aftermath of the Synod's vote last month, what was startling was how many people who certainly wouldn't have said 'yes' to the census question turned out to have a sort of investment in the Church, a desire to see the Church looking credible and a real sense of loss when - as they saw it - the Church failed to sort its business out."

He went on to say: "If people hesitate to call themselves Christian, perhaps this is a sort of backhanded recognition that there is a strangeness and a toughness to what Christian faith claims that should not be taken lightly.

"And yet, if many people still do, in spite of everything, want to call themselves by the name Christian, that also means there is a recognition that somehow this is where we should be, where it's natural to be - in the company of this man, Jesus Christ, listening to his words, turning aside to see deeply into the mysterious events of his life and death and resurrection.

"We are, after all, doing something rather outrageous, asking men and women to stop and look and turn around, and learn how to keep company with a figure whose outlines we often see only dimly."

Speaking of his time as archbishop, he said: "When people respond to outrageous cruelty and violence with a hard-won readiness to understand and be reconciled, few if any can bring themselves to say that all this is an illusion.

"The parents who have lost a child to gang violence, the wife who has seen her husband killed in front of her by an anti-Christian mob in India, the woman who has struggled for years to comprehend and accept the rape and murder of her sister, the Israeli and Palestinian friends who have been brought together by the fact that they have lost family members in the conflict and injustice that still racks the Holy Land - all these are specific people I have had the privilege of meeting as archbishop over these 10 years."

The challenge is for everyone, he said, adding: "Go and join the rest of the human race and acknowledge who you are. That's the truest heroism and the hardest."

Meanwhile, Bishop Welby used his Christmas Day sermon to say "the main job of the Church is never self-preservation, but glorifying God".

He told Durham Cathedral: "It is very easy to be despondent about the Church.

"Some speak of division and even of betrayal. The processes we go through are agonisingly wounding for many.

"There are profound differences of opinion about the nature of Christian truth and its place in society, about the right of an ancient tradition to dictate or even to advocate ethical values around the end of life, around marriage, around the nature of human relationships, inequality, our duty to each other."