high correlation among interaction terms

Y= alpha+ b1*x1 + b2*x2 + b3* x3 +b4*x4 + b5*dummy1*x1+b6*dummy1*x2 + b7*dummy1*x3 +b8*dummy1*x4

I run the correlation between all the regression variables and I found that all variables that are multiplied by dummy1 are highly correlated (correlation can reach up to 0.77). is this normal when I use many interaction terms based on the same dummy or should I resort to something to solve multicolinearity (such as orthogonalizing dummy1*x1 on dummy1*x2 etc....)