The Grand Lodge of Scotland plans a "British Together" parade and rally in Edinburgh on September 13 - just days ahead of the referendum.
Better Together has already distanced itself from the Orange Order, which has officially registered as a "permitted participant" in the referendum. Yesterday marchers carried pro-Union banners throughout the parade.
Jim Murphy, the Labour MP for East Renfrewshire and former Scottish Secretary who is travelling through Scotland with his "100 towns in 100 days" tour on behalf of Better Together, said the Orange Order was an "unsavoury" organisation, adding: "Not for a moment would they be part of the Better Together campaign. They'd be unwelcome."
Yesterday's annual County Grand Orange Order parade in Glasgow saw Orange lodges and loyalist flute bands taking part. But there were ugly scenes when their supporters were involved in violent scuffles which left at least one person badly injured.
A young woman received a serious head wound and was given medical treatment at Glasgow Green where those taking part in the parade and their supporters gathered after marching through the city. Eighteen people were arrested. Police said the arrests related to disorder, drinking in public and minor offences.
Around 4500 marchers took part with 4000 spectators. One eyewitness at Glasgow Green, who was not a participant and did not want to be named, said trouble broke out amongst a group of 25-30 spectators after the marchers congregated.
"I couldn't say what had happened to the young woman, but people around said she had been bottled," he said. "I heard voices getting raised and the next thing it all blew up, you could see fists and stuff flying about.
"The mounted police came in and as it started to disperse I saw this girl out the corner of my eye coming across the grass screaming.
"It looked like she was cut across her forehead, there was a lot of blood. It was a clean cut and she looked like she was about an inch away from losing her eyesight. I think she was just unlucky to be caught up in it."
It is understood the young woman was part of a family group watching the parade. Police had earlier warned sectarian behaviour and drinking in public would not be tolerated.
Trained stewards accompanied the march, freeing police to concentrate on street drinking, drunkenness, and anti-social behaviour - in particular sectarian behaviour.
Police Chief Superintendent Andy Bates said: "This event is one of the biggest policing operations the division manages on an annual basis.
"Our priority is to make sure the parade is peaceful with the safety of those taking part, the general public and officers, being paramount. I recognise that it is not the people taking part in the parade who cause trouble but an unwelcome minority who turn up and use the event as an excuse to drink, cause offence and behave in a manner which cannot be tolerated in our communities. It is these people that my officers will focus on, targeting violence, disorder and anti-social behaviour."
Police Scotland said it worked closely with the Orange Order and Glasgow City Council to agree a route for the march and to minimise any disruption to the city centre.
Officers and stewards were stationed along the parade route to help with traffic restrictions.
Edward Hyde, County Grandmaster of Glasgow and Grand Secretary of the Orange Lodge of Scotland, said he was aware of the incident at Glasgow Green and said he had been told by the police it was "nothing to do" with the Orange parade.
He blamed the trouble on what he called "the blue-bag brigade" in reference to fact that some followers of the parades are seen carrying alcohol in off-licence bags.
He said the Orange Order was training stewards to "identify troublemakers and make the troublemakers known to the police - we are quite willing to do that."
He added: "We are also taking it a step forward to involve the bands and try to get them to dissuade the bad elements. If you were in the town today there was an awful lot of families there, waving the Union flag and it was a family event. These people - the blue bag brigade - are a total embarrassment to us."
He added: "We are doing our best to rid ourselves of that element and we will get there - we are working very hard."
Referring to marchers carrying No banners, Hyde said: "Being a pro-Union organisation we obviously took the opportunity to get our message out."
Another senior Scottish Orangeman, Ian Wilson, former Grand Master and currently on the Orange Order's planning committee said: "Our rally on September 13 has been two years in the planning and so we certainly intend to go ahead with it ... The rally in Edinburgh is intended to be a celebration of Britishness. We are proud to be Scottish and proud to be British and the event will look very much like a Lodge parade but with carnival elements."
In an interview with the Sunday Herald before yesterday's walk, Labour MP and prominent No campaigner Jim Murphy said: "I've never had anything to do with the Orange Order and I'm never going to have. Not for a moment would they be part of the Better Together campaign. They'd be unwelcome."
He claimed that "other faith organisations … appear to be all-welcoming. The Orange Order exist for a different purpose. Their unsavoury history ... no matter how you slice and dice it ... it's not an inclusive organisation. They've got a vote so they should have a voice, right? But we'll find no common cause with them."
Better Together said: "This organisation isn't part of our campaign and never will be. The best way for people who believe that we are stronger and better together as part of the UK to get involved is by speaking to undecided voters, not marching in the streets."