Despite payment company Square's recent moves with bitcoin, the growth of its mobile payment app has been immune to the cryptocurrency's price nosedive, according to Nomura Instinet.

Square Cash, which officially launched crypto trading in late January, has been able to “decouple” from bitcoin and is growing roughly three times faster than Paypal's Venmo, with nearly 2 million downloads per month in May and June, according to a Nomura analysis.

"Square is more than just a bitcoin play," Dan Dolev, executive director and analyst at Nomura Instinet, told CNBC. "A lot of people were worried because it went up with bitcoin, but instead it's decoupling."

A spike in bitcoin prices late last year helped explain a surge in Cash App downloads growth around December, when bitcoin was nearing $20,000 and Square first announced it was testing support for bitcoin, Dolev said. Bitcoin prices have dropped more than 65 percent since that peak.

But as bitcoin has struggled, the Cash App’s growth has accelerated. Download rates were particularly strong in May and June, when bitcoin's price fell 19 and 15 percent, respectively. The app’s downloads rose 154 percent year over year for May and 153 percent in June, Dolev said.

As a benchmark, Nomura Instinet compared Square Cash monthly downloads with those of popular cryptocurrency exchange Coinbase, which according to Dolev have turned sharply negative in recent months. In June, for example, Coinbase’s monthly download growth fell 39 percent, according to Nomura's research.

In June, Square, which is run by Twitter CEO Jack Dorsey, got the green light from regulators to allow New Yorkers to trade cryptocurrency on the Cash app. But that didn't have a material effect on downloads.

"When they opened up trading in New York, you would expect a bump in downloads, but it didn't happen — if you look at the weekly trend it actually slowed slightly," Dolev said.

Square Cash is about 200,000 downloads shy of Venmo’s total 31.4 million, according to Nomura. Based on growth, the Cash App downloads are on track to exceed Paypal’s Venmo within a couple of weeks, Dolev said.

The firm has a "buy" rating and an $82 price target for Square, roughly $17 above where it was trading Wednesday. The stock is up 86 percent this year, and 154 percent year over year. To be sure, Nomura said Square's ability to achieve its target could be affected by pricing pressure, slowing gross payment volume and new offerings entering the market from competitors.

Bitcoin traded near $6,300 Wednesday and has fallen more than 55 percent this year after climbing more than 1,300 percent in 2017, according to data from Coindesk.