Zynga, the largest maker of social games on Facebook, has filed papers to raise $400 million in a secondary public offering. The money will go to shareholders.

According to a filing with the Securities and Exchange Commission, certain shareholders will sell their stock in the offering, but Zynga itself will not sell any shares and will not receive any proceeds from the offering.

The purpose of the offering is to facilitate “an orderly distribution of shares and to increase the company’s public float.” The latter means to have more shares available for the public to buy. Morgan Stanley and Goldman Sachs  Co. will handle the offering, while BofA Merrill Lynch, Barclays Capital, J.P. Morgan Securities and Allen & Co. will assist. The pricing of the offering hasn’t been set yet.

As VentureBeat reported yesterday, the implicit purpose of the new offering is to let Zynga investors sell stock while getting large shareholders to agree to a longer lock-up period that stops them from dumping shares. Typically, employees and other shareholders are allowed to sell their stock about six months after an IPO, which often leads to a dip in the stock price as the market becomes flooded with sellers. The secondary IPO could reassure investors that employees won’t dump their stock as soon as they are able.

Zynga previously raised $1 billion in December through its initial public offering.

The maker of games such as CityVille and FarmVille, Zynga has more than 240 million monthly active users on Facebook, and it has generated more than $1.85 billion in revenue since its founding in 2007, the filing says.

The names of selling shareholders won’t be available until later. Michael Pachter, analyst at Wedbush Securities, said the offering could be positive for Zynga’s stock price because it will result in staggered lock-up release dates for inside shareholders.