The U-turn comes after 1,800 viewers complained to the corporation.
Viewers vented their fury about the voting bungle on BBC message boards after it was decided that all three remaining contestants, Lisa Snowdon, Rachel Stevens and Tom Chambers, would contest this week's final.
A tied judges' decision meant Chambers could not be saved from the dance-off by the public vote.
The programme makers have devised a new voting system for this week's final, in which the combined scores of the judges and viewers will carry over from last week.
In an unprecedented move, and a bid to show transparency, the BBC will begin the first of two shows by disclosing the total marks allocated to each of the contestants so far.
Each couple will dance and the scores will be added to last week's tally. The couple that score the lowest overall will leave the competition.
In the second show, the two remaining couples will start from scratch and only the viewing public will decide the winner.
Refund details will be available on the BBC website, but that may not be the end of it. Media regulator Ofcom has also received complaints and may launch an investigation.
.jpg)
.jpg)