Greenlight's dual-class stock would have split common shares into one class that would concentrate on dividends paid to investors based on GM's healthy profits, $2.6-billion net in 2016, and one that would "reflect GM's growth potential", according to Reuters.
"We chose to bring a creative idea to GM's shareholders and nominate directors to help fix GM's inefficient capital structure and unlock significant value for all shareholders", Einhorn said in a statement Tuesday.
"We value the perspectives of our shareholders and will continue to actively engage with them", she said.
GM stock has risen little since its initial public offering in 2010, hovering just above $33 per share.
GM's chief executive Mary Barra though, had said to shareholders that there was no evidence Greenlight's proposal will work and there may not be any demand for the new stock.
GM has encountered various speed bumps since Ms. Barra took over for Dan Akerson, an auto industry outsider who was appointed to GM's board during the government-funded bankruptcy of the company in 2009. He congratulated the management team on its latest "win".
Barra reiterates GM's plan to allocate capital at home and overseas only where there is evidence of future return on investment, evidenced by decisions to exit unprofitable markets such as Europe with its divestiture earlier this year of longtime German unit Adam Opel.
"We are continually working to make our business more efficient and remove costs", Barra said during a press conference in Detroit prior to the company's annual meeting. Einhorn's Greenlight Capital hedge fund owns 3.6 percent of GM.
"We're are aggressively returning capital to shareholders, we're deploying resources in higher return opportunities, we're delivering great new cars, trucks and crossovers.and we're working to lead the transformation of personal mobility", she said.
Barra touted the the company's Bolt electric vehicle, acquisition of autonomous driving startup Cruise Automation as well as recent decisions to exit underperforming countries as moves that the company hopes will pay dividends on Wall Street. The company's nominees were backed by 84% to 99% of holders.
Nine of 11 directors in the GM board are independent, plus Barra and former UAW Vice President Joseph Ashton, appointed by the UAW Trust.
Greenlight's three candidates for the board of directors were Leo Hindery Jr., a veteran telecommunications industry executive; Greenlight executive Vinit Sethi; and William N. Thorndike Jr., managing director of Housatonic Partners, a private equity firm.