Vodafone investors are hoping Sir Christopher Gent's resignation as honorary life president will restore some harmony to the firm.
Analysts hope Sir Christopher's departure will help calm tensions
The ex-chief executive quit on Sunday after rumours of a boardroom spat.
Chairman Lord MacLaurin's statement backing current chief Arun Sarin should also help ease tensions at the firm, observers said.
Recent reports had suggested that the firm's so-called "old guard" had been trying to squeeze out Mr Sarin.
Tension had reportedly risen following a number of announcements from the firm.
Earlier this month Vodafone said it was in talks about selling its struggling Japanese phone business.
And last month it warned its assets were overvalued by as much as £28bn, and said that it faced slowing revenue growth. That news drove its shares to three-year lows.
Analyst Nick Hodson of Lloyds TSB said shareholders had been disappointed with Vodafone's recent performance as "not much had happened" since Mr Sarin took charge of the firm.
"Under Sir Chris, Vodafone was a mammoth and gobbled up practically anything in its way and it's left a lot of companies in its wake," he told the BBC.
In a statement released on Sunday, Lord MacLaurin gave his full backing to Mr Sarin, saying he had read reports of a rift with "great concern".
"I want to make it clear that I and the board are totally supportive of our chief executive... as he takes the company forward in changing and challenging times," the statement added.
"Any other suggestion is completely untrue."
Meanwhile, Sir Christopher said he had decided to relinquish his honorary position - which has no executive or advisory responsibilities - following the rumours.
Any claims he had used his post to interfere in the running of the company were "without foundation", he added.
In an interview on BBC Radio 4's Today Programme, Charlie Pretzlik, companies editor at the Financial Times, said Sunday's developments should go some way to restoring investor confidence.
But he added that the "outbreak of unity" at Vodafone should not be taken at face value.
"It's quite interesting that Lord MacLaurin while on the one hand said he and Sarin were... totally united he stopped short significantly of denying that he had harboured misgivings about Sarin," Mr Pretzlik said.
He added that what investors would want now is a clearer strategy from Mr Sarin about his plans for the future.
"He (Mr Sarin) is beginning to think about whether or not the company needs to own all the assets in all the parts of the world and whether it can reverse a bit of the big global strategy," Mr Pretzlik said.
"I think if Vodafone can be a little bit clearer about that then the shareholders will be encouraged."