There are plenty of stories about the gritty determination of Jack Dorsey, who has started two of the Web’s most influential firms. But could the Twitter founder’s strong character be the reason for Square chief operating office Keith Rabois leaving his post today?

As All Things D reports, the US payments firm has announced the departure of its COO without explanation. The tech blog cites sources who claim that former PayPal and LinkedIn executive Rabois fell out with company founder Dorsey, and that ultimately led to his exit.

It’s not clear whether the “disagreements” between the two were related to any specific topic. For his part, Rabois — who was with the company for two and a half years and is an angel investor — gave a statement that provides little explanation for his departure, other than to tease his next project.

It is amazing what Square has accomplished since August of 2010. When I joined, there were 17 engineers all reporting flatly to Jack. The local coffee shop served as our interview room. Leading our amazing crew has been the most rewarding professional journey of my life. I am forever grateful to Jack, for his confidence in me and to each and every member of the team for allowing me to learn from them.

But every day matters. And it is better at this point for me to be doing something different every day.

As a result, I’ve decided to resign from Square. I am very excited about what lies ahead for the company. Square could not be better poised for greatness.

I will have more to share about my next opportunity soon.

The announcement includes comments from Dorsey that praise Rabois for his contribution, noting that the company “couldn’t have [grown] without him”.

Square has made COO Sarah Friar its acting CFO as it actively hunts for a replacement. It goes without saying that it will want bring in a new hire for this key position as soon as possible, to minimize disruption.

Last year was a huge one for Square as the company raised its Series D round, which included a $25 million investment from Starbucks and valued the firm at $3.25 billion. Its business footprint increased too as its partnership with the coffee giant saw its payment system go live in 7,000 Starbucks chains across the US.

The company last year announced it was processing $10 billion in annual payments, and that’s a figure that grew by $2 billion between September and November alone. With the Starbucks agreement already seeing rollouts, that number is likely to increase significantly this year. Now Square needs a COO to ensure that happens.

Headline image via cdharrison / Flickr