How to get smooth contour plot using any interpolation scheme?

I am trying to plot the contours of using spline cubic interpolation method. The problem I have that I don't get smooth contours lines. Any help will be appreciated. Here is my code:

clear all;
clc;
data = xlsread('Trial1.xlsx');
rlt = data ;
[height, width] = size(data);
[x,y] = meshgrid(0:5:width,0:5:height);
x(:,1) = 1; y(1,:) = 1;
z(1,1) = data(1,1);
for i = 1:height/5
    z(i+1, 1) = data(5*i, 1);
end
for j = 1:width/5
    z(1, j+1) = data(1, 5*j);
end
for i = 1:height/5
    for j = 1:width/5
        z(i+1,j+1) = data(5*i,5*j);
    end
end
[x1,y1] = meshgrid(1:width, 1:height);
z1 = interp2(x, y, z, x1, y1, 'spline');
for i = 1:height
    for j = 1:width
        if ~(data(height-i+1,j) > 0 )
            rlt(i,j) = z1(height-i+1,j);
   else
            rlt(i,j) = data(height-i+1,j);
        end
    end
end
% figure; mesh(x1,y1,z1); xlabel('longitude'); ylabel('latitude');
% F = [.05 .1 .05; .1 .4 .1; .05 .1 .05];
% ZC = conv2(rlt,F,'same');
xlswrite('digital_value.xlsx', rlt);
figure;
%contour(rlt,20);
[C,h] = contour(rlt);
clabel(C,h);
set(h, 'LevelList', [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19], ...
       'TextList', [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19])