A soy protein product having a protein content of at least about 60 wt % (N×6.25) d.b., preferably an isolate having a protein content of at least about 90 wt % (N×6.25) d.b., is formed by extracting a soy protein source with a salt solution, preferably aqueous sodium chloride solution, to form an aqueous protein solution having a pH of about 1.5 to 11, preferably about 5 to about 7 and separating the resulting aqueous protein solution from residual soy protein source. The protein concentration of the aqueous protein solution is increased to about 50 to about 400 g/L while the ionic strength is maintained substantially constant by using a selective membrane technique. The resulting concentrated protein solution is optionally diafiltered and a calcium salt, preferably calcium chloride, is added to the concentrated and optionally diafiltered protein solution to a conductivity of 15 to about 85 mS. Precipitate formed as a result of the calcium salt addition is removed and the resulting clarified retentate is diluted into about 2 to about 20 volumes of water prior to acidification to a pH of about 1.5 to about 4.4 to produce an acidified clear protein solution. The acidified clear protein solution is then concentrated and optionally diafiltered and optionally dried. Variations of this procedure can be used to produce a soy protein product which is soluble, transparent and heat stable in acidic aqueous environments.